He was educated at Magdalen College School in Oxford and studied at the University of Bristol and Prague's Charles University before becoming Central Europe correspondent for The Guardian and later the BBC. He specialised in reporting on the Yugoslav wars in the early 1990s that followed the breakup of Yugoslavia. While at the BBC, Glenny won 1993's Sony Gold Award for his "outstanding contribution to broadcasting". He published three books about Central and Eastern Europe.

Glenny is an executive Producer of the BBC One eight-part drama series, McMafia, inspired by his non-fiction book of the same name (2008).

Glenny's later books continue an interest in international crime. DarkMarket (2011) concerns cybercrime and the activities of hackers involved in phishing and other activities. Nemesis: One Man and the Battle for Rio (2015) about the leading Brazilian drug trafficker Antônio Francisco Bonfim Lopes (known as "Nem") in Rocinha ("Little farm"), a favela (slum).

Since January 2012, Glenny has been visiting professor at Columbia University's Harriman Institute, teaching a course on "crime in transition". In an interview in October 2011, he also spoke about his new book, DarkMarket; assessing cybercriminals with Simon Baron-Cohen at Cambridge; the Stuxnet cyberattack which resulted in "gloves off" attention from governments; and other more recent cyberattacks.

Glenny is married to British Journalist and broadcaster Kirsty Lang and has three children, two with his first wife (their daughter took her own life in 2014) and one with Lang.