Glenny is the son of the late Russian studies academic Michael Glenny. He was educated at an independent school, Magdalen College School, in Oxford, and studied at Bristol University and Prague's Charles University before becoming Central Europe correspondent for The Guardian and later the BBC. He specialised in reporting on the Balkans independence wars in the late 1980s and early 1990s that followed the collapse of Yugoslavia. While at the BBC, Glenny won 1993's Sony Gold Award for his 'outstanding contribution to broadcasting'. He has also written three books about Central and Eastern Europe. His latest book McMafia (2008) is about international organised crime, which, he writes, may now account for 20 per cent of the world's GDP.

Glenny advised the US and some European governments on policy issues and for three years ran an NGO helping with the reconstruction of Serbia, Macedonia and Kosovo.

Glenny is married to the journalist and broadcaster Kirsty Lang and has three children, Miljan and Sasha Glenny (from his first marriage), and Callum Lang.