Relic originally announced that Dawn of War III was in early development in 2011, just before their publisher, THQ, went bust. A period of confusion followed as Sega snapped up Relic and spent some time sorting out the various licensing issues. Games Workshop has branched out in the meantime, allowing numerous other studios to work on Warhammer and Warhammer 40,000 games. Battlefleet Gothic, a space strategy game set in the WH40K universe, was released just a few weeks ago and Total War: Warhammer will be released at the end of this month.
Dawn of War III was originally mooted a multiplayer-focused title. It is unknown if this is still the plan or if the game will have a single-player campaign as well. In addition, it is unknown if the game will be a large-scale strategy game with base-building, like the original Dawn of War, or something more reminiscent of Diablo, as (highly controversially) was Dawn of War II. Relic's press hints that the game will hew closer to the original but it is unclear how much. From the trailer it looks like the game will focus on the Space Marines, Orks and Eldar as the initial factions, and the game will allow the deployment of Titans (massive armoured battle-mecha, hundreds of feet tall) in some fashion.
No release date has been announced, but the end of this year is likely the earliest release window.