(written from a Production point of view)
Paramount+ (formerly CBS All Access) is a digital subscription video on demand and live streaming service allowing access to CBS, BET, Comedy Central, MTV, Nickelodeon, and Smithsonian Channel shows past and present, including every Star Trek series.
Launched on 28 October 2014 as CBS All Access in the United States, the service – operated by CBS Interactive – expanded to Canada on 23 April 2018 and planned to expand into Australia in late 2018 (although, due to existing rights agreements, not all of the service's programming accompanied the expansions).  
In November 2015, CBS Corporation President and CEO Leslie Moonves revealed that, as a result of the various Star Trek series performing "exceedingly well" on CBS All Access, Star Trek: Discovery would premiere exclusively on All Access as the service's first original series (although The Good Fight ultimately aired first). Moonves characterized the decision as a means to entice "millions" of new subscribers.  When Discovery premiered on the service in September 2017, "record-breaking" single-day signups were reported,  though viewership numbers have never been disclosed by either the franchise or its owners, then or anytime later.
The first Discovery companion series, After Trek, also aired on the service, as does Star Trek: Short Treks, Star Trek: Picard, Star Trek: Lower Decks, and the second season of The Ready Room, the follow-up to After Trek. The forthcoming Star Trek: Strange New Worlds, and the Untitled Section 31 series will air on the service as well.  
Besides the various Star Trek productions and The Good Fight, original programming includes No Activity, Strange Angel, One Dollar, and Tell Me a Story (starring Kim Cattrall).
Besides original programming, the service also streams the annual Grammy Awards and games of the National Football League (NFL).
In January–February 2021, a series of commercials featuring Paramount Mountain aired advertising the transformation of CBS All Access into Paramount+. They featured Sonequa Martin-Green as Michael Burnham, Captain Christopher Pike played by Anson Mount, Spock played by Ethan Peck, and Patrick Stewart as himself. Other actors and voice actors appearing or heard included Bryson DeChambeau, Gayle King, James Corden, Jeff Probst, Jimmy Kimmel, Snooky, Stephen Colbert, and Trevor Noah. Music was the song "Sweet Victory," performed by David Eisley and Bob Kulick.
On 4 March 2021, CBS All Access was rebranded as Paramount+. 
In November 2021, Paramount+ was announced as the exclusive broadcaster for Star Trek: Discovery in all markets except Canada, following the removal of the program internationally from Netflix. The move, made days ahead of the premiere of the program's fourth season, was met with widespread fan outrage, as it was stated that the program would no longer be available in those markets until 2022. On 24 November, 2021, it was announced instead that the program would be made available instead on 26 November, 2021 in all markets in which Paramount+ had already rolled out, with new episodes instead premiering on Pluto TV in other markets in which the service is not yet available.