Głowacki left Poland when martial law was imposed in December 1981 and continued working in the UK and later in the US. After 1990 he divided his time between New York and Warsaw.

His most acclaimed stage plays were written in the US: Hunting Cockroaches, Antigone in New York and The Fourth Sister. His most important film contributions are the scripts for Andrzej Wajda’s Hunting Flies (1969) and Wałęsa: Man of Hope (2013, Akson Studio).

His distinctions include the American Theatre Critics Association Award, the John S. Guggenheim Award, the Hollywood Drama-League Critics Award, the National Endowment for the Arts, the Jurzykowski Prize, the Czesław Miłosz Award and the Warsaw Literary Prize.