(written from a Production point of view)
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. CBS acquired the rights to Viacom's Paramount Television, which was subsequently renamed CBS Paramount Network Television (now known as CBS Television Studios) and to UPN which subsequently merged with The WB to become The CW. CBS Corporation also continues to own Simon and Schuster and Paramount Parks, which previously fell under Viacom.
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.