Reuters reports an unidentified source in Russian law enforcement agencies as saying on Monday (via Interfax and Itar-Tass) that Caucasus Emirate leader Dokka Umarov has been killed by Russian forces "on the territory of one of the republics of the North Caucasus".
Axisglobe now says that according to Russian sources the body has not yet been identified,
In 2006 the Moscow-backed Chechen government claimed that Umarov had surrendered, though this proved to be erroneous.
On June 4 Russia's Channel One reported that President Dmitry Medvedev held a meeting with FSB Director Alexander Bortnikov - the current situation in the North Caucasus was at the top of the agenda, and Bortnikov is thought to be under pressure to achieve results.
Update: Reuters (via Moscow Times) has Ramzan Kadyrov saying that Umarov was severely wounded -- "too early to say" whether he was killed.