(written from a Production point of view)
CBS Consumer Products, Inc. is the licensing and merchandising unit of CBS Entertainment which manages the licensing of products for the various television shows owned by CBS, CBS Television Studios and CBS Television Distribution. This company controls the licensing to produce all Star Trek DVDs, novels, games, toys, clothing, and merchandise.
The company also collaborated with Mad Science to develop Star Trek Live, an interactive stage show which opened in 2010 and continues to tour today. Star Trek The Exhibition was also co-produced by the company. Products branded with the CBS Consumer Products name have also been released by The Bradford Exchange, The Hamilton Collection, Hammacher Schlemmer, and ThinkGeek, among others.
The unit also doubles as an archive for the Star Trek merchandise they have licensed – some of which actually turning up in various live-action productions such as, aside from Star Trek proper, The Big Bang Theory – as well as serving as a repository for the original live-action production documents and art that have been created throughout the history of the franchise, thereby functioning as a reference source for authors of licensed reference works, though a considerable amount of the latter has been sold off in the 2006-2008 wave of Star Trek auctions. (source)
Established in 1967 as part of the newly formed Paramount Television division (the former Desilu Studios), while Star Trek: The Original Series was in production, the unit was known as the "Paramount Publicity Department", headed by Howard McClay and Frank Wright, and it were they, aside from handling the legalities surrounding contemporary Star Trek merchandise, who provided author Stephen Edward Poe with the illustrative material for the first Star Trek reference book, The Making of Star Trek. Poe also had professional dealings with the department, as he was the account manager for model kit company AMT in regard to their Star Trek model kit line. (p. 15)
Until 1979 merchandising and licensing was a rather passive and haphazard affair. Interested parties had to approach the department with proposals, which the department's involvement somewhat limited to either agreeing to them or not, and drawing up contracts. However, when Star Trek: The Motion Picture was in production, the department, now called the "Paramount Marketing and Licensing Department" (still covering both the television as well as the movie properties of the studio) made a quantum leap forward in professionalism.
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The leap forward was necessitated by the February 1979 visual effects crisis during the movie's production, and responsible for the leap was the department's newly appointed Vice-president Dawn Steel. Steel was charged with creating another revenue stream to help cover the ballooning production costs. She did so by organizing a vigorous merchandising and licensing fund drive, which climaxed in a highly imaginative presentation, held in the largest theater on the Paramount lot. A resounding success, the presentation was met with rambunctious enthusiasm by the attending prospective licensee companies. "It was the most unbelievable party Paramount ever had.", attending studio producer, Brian Grazer, remembered, to which then novice studio producer Jerry Bruckheimer has admiringly added, "She went to conventions and got every toy-maker, anyone who made T-shirts and key chains and raised every nickel she could. She shook the trees. There hasn't been that energy vortex in merchandise since she left.". Numerous companies signed up, including, at the time, unusual ones such as food industry corporations like Coca-Cola and McDonald's. The presentation marked the first time for Paramount that licensing revenues were generated, before a production had premiered. The successful fund drive made Steel's name in the motion picture industry, and a thoroughly impressed Paramount CEO Michael Eisner, who was (in)famous for not being easily impressed, promoted her the next day to vice-president of productions in features, getting her off to a stellar industry career. She had been working in the licensing department for less than six months. (New York Magazine, 29 May 1989, p. 45; 6 September 1993, p. 40; Star Trek: The Complete Unauthorized History, pp. 108-109)
Concurrently, parent company Gulf+Western had commissioned the development of an accompanying, The Motion Picture-themed, book line, through subsidiary Pocket Books, which it had acquired in 1975 (and therefore a sister company of Paramount Pictures), and from here on end merchandising and licensing became an integral part of a proactive overall marketing strategy (considerably hammered out by Frank Mancuso, Sr., who was hired as the department's president after Steel had left), in the creation of a sustained Star Trek product line. 
A somewhat ambiguous situation arose in 2005, when the original Viacom holding corporation was split up into two independent corporations, the television corporation CBS Corporation (which constituted the former Viacom) and a motion picture corporation, which, a bit confusingly perhaps, was called Viacom (new) and of which Paramount Pictures was now a part. CBS has licensed the right to produce Star Trek films to Paramount Pictures, but CBS Consumer Products remained the sole entity responsible for the marketing and licensing of the Star Trek product line for both the television as well as the movie properties, instead of farming it out to Paramount's own division, Paramount Licensing, Inc.