Pressure from the Iraqi Communications and Media Commission has meant that the show is no longer broadcast in Iraq, although citizens are able to access the programme online.
In 2011, after being injured in a suicide bombing in which his friend was killed, Albasheer left Iraq and moved to Amman, Jordan, where he set up his own production company, Lagash, in 2012.
Albasheer Show draws its satire from new stories, political figures, and media organisations, and often criticises the ongoing issues of corruption, sectarianism, extremism and terrorism in Iraq.
Albasheer, whose father and brother were killed during the Iraq War, and who was himself kidnapped and tortured in 2005, has stated his experiences heavily influenced the shape and content of the show, commenting "instead of getting revenge with a weapon, I try to fix the situation so nobody has to go through the things I went through.
One consistent target for mockery on the show has been the Islamic State, which controlled the city of Mosul between 2014 and 2017, who made several death threats against Albasheer as a result.