That question opens up a whole can of worms, but the short version (and it's complicated, so I may have missed something).
FASA Corp. publishes Shadowrun 1st. edition in 1989.
In 2001 (now in 3rd edition), FASA effectively closes shop, but licenses its various IPs.
Weisman, through Smith & Tinker, holds the video game rights and licenses them to Microsoft, who puts out a FPS in 2007 no one is allowed to talk about.
WizKids buys the Shadowrun IP and licenses it to FanPro.
FanPro is bought by Topps in 2003.
FanPro releases 4th edition in 2005.
In 2007 FanPro gave up the license to Shadowrun RPG material (my understanding is they still have the license for English fiction, but may be wrong about that).
Topps then gives the license to Catalyst.
Catalyst releases 20th Anniversary edition in 2009.
In 2012 Weisman has a Kickstarter campaign and buys back licenses the video rights from Microsoft, later releasing Shadowrun Returns.
In 2013 Catalyst releases 5th edition.
It's fair to say that some of these moments were unexpected and fairly dramatic and contributors have...mixed...feelings about some of the previous IP holders, but that's the bare bone version.