After obtaining a BSc(Hons) from Institute for Molecular Biology (IMB) at the University of Queensland, Professor Thompson undertook a PhD at the MRC Laboratory for Molecular Biology at the University of Cambridge, where he learned Drosophila genetics. Professor Thompson then worked as a postdoc at the European Molecular Biology Laboratory (EMBL) in Heidelberg, Germany, where he used Drosophila genetics to study Hippo signalling and tumour formation, and visited the Research Institute for Molecular Pathology (IMP) in Austria to perform a large scale RNAi screen in Drosophila.

He established his own laboratory at the Cancer Research UK London Research Institute (LRI) in 2007 and began his studies on genes that control tissue growth and form in Drosophila and mouse models. The LRI became part of the newly founded Francis Crick Institute in 2015, where Professor Thompson became a Senior Group Leader and Wellcome Investigator. He moved to become an EMBL Australia Group Leader at the John Curtin School of Medical Research (at the Australian National University, Canberra) in 2019.