UNIX development truly began in the 1960's under the name Multics, a project that yielded little monetary results and was abandoned by one of the major companies that contributed to its development. However, work on the project was continued by some of the individuals involved and eventually culminated in the birth of Unics (a play on "Multics", later renamed to UNIX) in the 1970's.
In the 1980s, AT&T implemented commercial licenses on UNIX distributions and streamlined all versions into one: UNIX System V. The University of California, Berkeley, continued development of its own version of UNIX, called BSD. Many of the significant developments in UNIX originally came from BSD - namely the inclusion of TCP/IP code in a major UNIX version.
Through the 80's and 90's, many companies commercialized and licensed their own versions of UNIX, including Sun Microsystems, Microsoft, and SCO, among others. Around this same time, groups of developers and companies began a hard push for "open" UNIX, creating a further branch in UNIX development. During the early 90's, AT&T sold all of their UNIX rights to Novell. In 1995 Novell sold some of their UNIX rights, including the right to further develop on System V, to SCO.
All of this buying, selling, licensing, de-licensing, and independent development of the 90's eventually led to law suits, disputes, and drama over who owned what parts of what UNIX. Linux was also thrown into the mix, as one lawsuit filed by SCO claimed that Linux contained copyright UNIX code that belonged to them. When everything was said and done, Novell won the case against SCO, and forced SCO to dismiss its lawsuits against IBM and Sequent, as well as Linux. They went as far as to say that "We do not believe that there is UNIX in Linux."
Today, Sun Microsystems' Solaris is the largest UNIX operating system. BSD has continued its development and has spawned free versions such as FreeBSD. In 2005 Sun released the majority of its code with OpenSolaris, which has led to even more versions of open source UNIX.