At the present point in time (the end of 2015), a legal ruling shows that Novell owns the copyrights to the Unix source code. This covers all code developed at Bell Labs, USL, AT&T etc. up to and including the latest version of System V. Other companies that have made and sold modified versions of Unix (e.g. IBM, Microsoft, Sun Microsystems) have copyrights on their versions of Unix.
Fortunately, much of the historical Unix source code, including the research versions up to 7th Edition and many of the BSDs, are available in the Unix Archive and are covered by the Caldera license. This is essentially a BSD license and allows you to read, modify and distribute the source code.
Unix has had a long a tortuous copyright and licensing history. Perhaps a short summary of the history can be placed here with links off to more detailed coverage of the history. You can find details of the journey to free Unix licenses here.