(written from a Production point of view)
The CBS Corporation is a major media conglomerate. They own CBS Studios which in turn is appointed the titular holder of the Star Trek trademark and all other Star Trek related marks and copyrights. Effectively, it is CBS Corporation that owns the Star Trek franchise.
The CBS Corporation was formerly known as Viacom. Following Viacom's split with CBS in 2005, Viacom dissolved and was re-established as the CBS Corporation with Les Moonves appointed as its head. CBS acquired the rights to Viacom's Paramount Television until then headed by Moonves, which was subsequently renamed CBS Paramount Network Television (now known as CBS Television Studios) and to UPN which Moonves subsequently merged with The WB (Warner Bros. and a previous employer of Moonves) to become The CW. CBS Corporation also continues to own Simon and Schuster and Paramount Parks, which previously fell under Viacom. One of CBS's other subsidiaries is magazine publisher CBS Communications, which publishes the The Official CBS Watch! Collector's Edition magazine series, in which three Star Trek-themed issues have been released, as of 2015.
Following the split, a new Viacom was founded. This company received the rights to Paramount Pictures, which includes production and distribution of the Star Trek films. The licensing of consumer products related to Star Trek is presently controlled by the CBS Consumer Products division.
CBS Corporation and the new Viacom are both controlled by National Amusements.