It's large and the third volume hasn't been released yet (it's supposed to come out this year), but Stephen Kotkin's trilogy is the most up-to-date Stalin biography. Volume I is Paradoxes of Power, 1878-1928, and Volume II is Waiting for Hitler, 1929-1941. Kotkin is a Soviet historian of notable repute, and his work synthesizes both archival research of everything available to date, plus other historians' research. He argues a few controversial points but overall covers the accepted general academic consensus on Stalin, and also includes a lot of contemporary history (so the books aren't just a straight biography).

Oleg Khlevniuk is also a respected Russian historian and has a one-volume biography: Stalin: A New Biography of a Dictator. Another one volume biography is Robert Service's Stalin from 2004. Service wrote this as part of a trilogy of biographies, including Lenin and Trotsky - the others have been criticized, but the most I see on the Stalin volume is that it doesn't come to life as well as it could.

Richard Overy is a British historian of World War II and wrote The Dictators, which is a comparative history of Hitler's Germany and Stalin's USSR. This covers their biographies and personal lives but also their public images and more general histories on both regimes.

A final mention should be made of Simon Sebag Montefiore's Court of the Red Tsar and its prequel Young Stalin. These lean very heavily into Stalin's personal and family life, plus the idea that Stalin is best understood as a Caucasian patriarch and mafia don.

Stephen Kotkin’s trilogy (well, the third book isn’t out yet) is pretty well regarded. Paradoxes of Power and Waiting For Hitler are the subtitles for volumes I and II respectively. These are very current and very authoritative. Melanie Ilič’s (ed.) Stalin’s Terror Revisited (2006) is also good. It addresses the purges beyond the urban political elite, in particular.

Thanks for the recommendations, everyone.