The Continuities of Star Trek
The live-action TV series and movies produced by Star Trek's copyright owners are canon by definition. Until 2009, all canon Star Trek was set in the same timeline (although owing to time travel it was frequently subject to subtle changes). In contrast, the Abrams movies explicitly take place in a detached timeline and hence in a new continuity. Although Star Trek Discovery is meant to exist in the same continuity as TOS, this official claim is hard to uphold, not only because it is a "visual reboot" but also because of numerous historical and technological facts that clash with classic Trek.
This article looks at the continuity of Star Trek and how the concept changed over time, from a single timeline to something like a multiverse. The article takes into account the official policy of CBS but also outlines a way to handle reboot series such as Discovery. Note that the purpose of this article is not to discuss whether or not the Abramsverse and Discovery are in contradiction to classic Trek, which I have already done in excruciating detail in several other articles and episode reviews and don't want to rehash here. Regarding the existing continuity issues, there are only summaries. Please follow the links to read a lot more about them.
Until 2009, all canon Star Trek took place in the same uninterrupted continuity. There is only one timeline that comprises (in production order) TOS (since 1964), the TOS movies, TNG, DS9, Voyager and Enterprise (until 2005). In chronological order, we have Enterprise (set in the 22nd century), TOS and TOS movies (23rd century) and TNG/DS9/Voyager (24th century).
Original continuity (until 2009)
Alternate continuities, such as changes to the timeline or parallel universes, have been an integral part of Star Trek's concept since the very beginning. However, all these other continuities have in common that they either don't persist or that they remain isolated from the one that the main storyline is set in. The only notable exception is the Mirror Universe from TOS: "Mirror, Mirror" that gets revisited several times. Past incursions via time travel may either lead to an undesirable transitory timeline that needs to be fixed (Nazi Germany winning WWII in TOS: "The City on the Edge of Forever"), or the changes are considered small enough to be allowed to persist (Sisko as Gabriel Bell in DS9: "Past Tense"). In consideration of the subordinate nature of alternate continuities in the storyline, it is appropriate to omit them and simplify the history of the Star Trek Universe until 2009 as a single timeline.
There is a certain deal of discontinuities between the single incarnations of classic Star Trek. Perhaps most notably, Enterprise, Star Trek's first prequel, is a series that introduces several 22nd century technologies that are just as powerful as in TOS or even TNG. It also shows us first contact with races that realistically couldn't have taken place in the 22nd century. The prime example for a visual change is that in "Star Trek: The Motion Picture" the Klingons look different than they did in TOS. While it may have been an option to disregard this particular discontinuity, it was explicitly hinted at in DS9: "Trials and Tribble-ations" and ultimately explained in ENT: "Divergence". In its fourth season, Enterprise went on something like a "continuity repair tour" that answered this and several more questions of how the series fits into the established history.
More generally speaking, classic Star Trek had the advantage that it could pass off real-life progress regarding its props and sets as an in-universe development as long as new series were sequels. But overall, every series, including the prequel Star Trek Enterprise, usually respected what had been established before. If inconsistencies came to pass, they were sometimes generously overlooked but not openly denied or glossed over (although at least ENT: "Acquisition" and "Regeneration" may be blamed for the latter).
Status of TAS
The Animated Series (TAS) is a special case, not because of continuity issues but rather due to its disputed canon status. Quality and compatibility concerns regarding this series are the principal reason why the producers as well as many fans are reluctant to accept it as fully canon. Continuity-wise, on the other hand, there are relatively few obstacles to a possible integration of TAS. Most notably, the Kzinti War (TAS: "The Slaver Weapon") can't possibly exist in the known continuity.
Regarding the films set in the Abramsverse (officially: the Kelvin Timeline), there is no doubt that they are canon, just like every live-action Star Trek. But they take place in a new persistent timeline, which constitutes a different continuity. In "Star Trek (2009)", Nero's time travel and the destruction of the USS Kelvin entails a chain of events with different technical histories (a completely different Enterprise is launched as late as 2258) as well as different personal histories (Kirk rises from cadet straight to captain) than in classic Star Trek. The divergence culminates in the destruction of Vulcan. From a merely technical viewpoint, the Kelvin Timeline is not unlike the various alternate universes that we already know from classic Trek. The decisive difference is that the narrative departs from what was considered the main ("Prime") timeline so far.
Official Prime vs. Kelvin continuity (as of 2017)
The story of "Star Trek (2009)", the appearance of Leonard Nimoy as Spock in the first two movies and the photo of the TOS crew in "Star Trek Beyond" firmly establish the Kelvin Timeline as one that branches off from the familiar ("Prime") timeline.
Roberto Orci, co-writer of "Star Trek (2009)", explained that in his idea the new timeline is a quantum universe much like the ones in TNG: "Parallels". In his view, it exists in parallel and does not replace the Star Trek that we know. This, of course, serves to pacify fans who are concerned that the old Star Trek is erased once and for all. Orci's theory, however, clashes with the depiction of time travel in classic Star Trek that always created a new timeline that replaced the old one and that compelled the characters to go back again and restore history.
The Abramsverse movies include more changes to the look and to technical principles of Starfleet than 25 years of divergent history could explain. The technology of the new movies is much more advanced than it should be (well, except for the engineering with riveted water pipes), starships including the Enterprise are a lot bigger than firmly established and the overall visual style has almost nothing in common with the one of TOS.
The technological and visual discrepancies are the reason why there are still different ways of how the fandom rates the continuity status of the films, in spite of Orci's clear-cut statement that a new parallel universe branches off when Nero destroys the Kelvin. Without further going into the details, many see it as a total reboot that has no ties with the classic Star Trek, much like it happened with Battlestar Galactica. Others presume that the timeline was different even before Nero traveled back in time, which may explain different technologies and huge ships but disregards the very story of the film.
The issue of what actually happens to the continuity is further complicated by a statement by Simon Pegg, who co-wrote "Star Trek Beyond". He suggested that the Kelvin Timeline may just as well extend into the past (a bit like in the fan suggestion about an earlier point of divergence but here apparently still caused by the Kelvin incident that for some reason affects the past as well). Yet, any canon evidence for such an unprecedented phenomenon is missing. It likely remains just a hypothetical possibility to grant future authors still more freedom to set new stories in any universe and any time they deem advantageous.
Star Trek Discovery is a whole new ballgame with regard to continuity. The series was conceived as a direct prequel to TOS, roughly ten years before Kirk would be in the captain's chair. The official position is that, quite unlike the Abrams films, the series is set in the very same continuity as TOS and the other classic Star Trek series.
Official continuity (as of 2019)
The first massive problem about Discovery is its totally new look, with changes relative to classic Trek (and also relative to the Abramsverse) that go very far beyond a reasonable "visual update". The Klingon make-up, their styling and their first-season starships are just the most blatant examples of a redesign from scratch, but Starfleet just as well doesn't look like it should ten years before TOS. We may decide to accept that Discovery is a "visual reboot", that it disregards an inherent principle of visual media, that looks have story relevance, unlike it is customary in novels. The visuals of Star Trek would be degraded to illustrations like the ones in a book that merely show an artist's interpretation of the story and that may be redone for a later edition.
Many more issues arise because of Discovery-specific people, historical events and technologies that don't exist in TOS or that shouldn't exist at all in the Star Trek Universe. In an attempt to regain the continuity with classic Trek, DIS: "Such Sweet Sorrow II" explains that the existence of Michael Burnham, the USS Discovery, the spore drive, the AI "Control", the time travel suit and possibly several more anti-canon aspects of the series will remain "classified", that no one is allowed to ever talk about them. In a similar fashion, the excursion to the Mirror Universe and Emperor Georgiou's true identity were already declared top secret at the end of the preceding season. It is neither realistic nor a desirable vision of the future that Starfleet would suppress the truth so rigidly. And that the Klingons would do the same. And that Spock would never talk to Michael Burnham, the sister he loved so much, even to his closest friend! And while the perfect secrecy is unbelievable anyway, it still leaves plenty of discrepancies that probably wouldn't fall under this ban, such as the holodeck, Klingon cloaking or the course of the war with the Klingons, to name only a few.
Discovery's re-interpretations have repercussions on the existing Star Trek. It is inconceivable that all Klingons of TNG, DS9 or Voyager, including Worf, suddenly have to look like the DIS Klingons - although this appears to be an equally valid or even the officially endorsed new interpretation. Or that the original USS Enterprise NCC-1701 has two different designs and two vastly different sizes. But that is the kind of doublethink the producers apparently expect from the fans. Even if we leave out visuals and think of Star Trek as an illustrated novel series, its continuity is impaired. Future viewers will have to watch TOS, TNG and the other classic series with the knowledge that important historical facts and technologies are kept under wraps. For instance, Voyager needed seven years and 168 episodes to finally find a way back into the Alpha Quadrant. This involved several "drives-of-the-week", which has become a commonly ridiculed trope of the show. But according to Discovery, a still much more advanced (and arguably more ridiculous) drive based on a fungal network and allowing instantaneous space travel, existed as long as 120 years earlier! It makes Janeway's efforts look stupid and pointless when we watch her show again.
A popular fan theory used to be that Discovery is the same continuity as the Kelvin Timeline, as ostensibly evidenced by the same design style (bridge windows) and the same type of effects (phaser bolts). But this idea was ultimately refuted in Discovery's season 2 that created clear ties to TOS by establishing that Pike and Spock were on the "old" Enterprise as of 2258, as opposed to "Star Trek (2009)" where Pike is an admiral, Spock is an academy instructor and a new Enterprise is ready for launch in the same year.
In roughly the same vein, there is a persistent rumor (allegedly coming from a "CBS insider") that Star Trek Discovery is produced under an "alternate license", the same license that also applies to the Abrams movies by Paramount and Bad Robot. This would technically make Discovery a part of the Abramsverse continuity, but as outlined in the preceding paragraph, rather not of the Kelvin Timeline. The rumor further gained momentum by the statement of a production designer, who said he was told to make all designs for the series "25% different" for legal reasons. Any further proof, however, is missing. There is no second source that would confirm the claims of the "CBS insider" or that would link it to the purported "25% rule". It is well possible that CBS officials or lawyers told the production people things that were not meant for the public. The "25% rule" may indeed have existed as some sort of internal guideline, to ensure that it fits with the producers' intentions to create their own new Star Trek.
The official policy is that Discovery is fully canon within the Prime Timeline, the only caveat being that it takes extensive liberties on the visual side. The reality is that the visuals and facts established in Discovery do not fit into the Prime Timeline continuity and even retroactively damage the existing series, and change their meaning in consideration of the new facts from Discovery.
Although it offends Discovery fans, some kind of "polluter liability" should be applied. TOS or TNG should not suffer from harmful facts established in Discovery, which could make the characters, Starfleet or the technology of the later 23rd or of the 24th century look dumb. Here at EAS, I respect the official position but I keep Discovery separate in a way that facts from Discovery have no influence on TOS and TNG. Discovery may be Prime Timeline, officially speaking, but it is a different continuity when it comes to facts established in the series. In some way, this is even the consequential continuation of the in-universe secretiveness about the USS Discovery, only that I extend it to the aspects of the series that may not fall under Starfleet's ban (whose exact extent is not clear anyway), as well as to visuals. So, as a provision to preserve the significance of the classic Star Trek, Discovery takes place in an isolated "Prime Reboot" continuity.
Practical continuity at EAS (as of 2019)
What is Canon? - definitions, reasons, interpretations and the EAS canon policy
The Visual Continuity of Star Trek - examples of if and how visual continuity was maintained through the generations
Star Trek (2009): Reboot or Multiverse? - thoughts on the continuity and the canon status of the movie
Dealing with Continuity Issues of the Abramsverse - general thoughts and the policy at EAS
Discovery Episode Reviews - with countless remarks on the (lack of) continuity of the series
Some screen caps from TrekCore.