Thompson has held visiting appointments at the Center for Subjectivity Research in Copenhagen, and at the University of Colorado, Boulder.
Thompson worked with Francisco Varela at CREA (Centre de Recherche en Epistemologie Appliquée) at the Ecole Polytechnique in Paris.
In this work, he combines insights from neuroscience, meditation and philosophy with his own biographical background and personal storytelling, including encounters with F. Varela and the 14th Dalai Lama.
Based on his theory that direct experience plays a primary role, Thompson advocates for the development of a contemplative neuroscience.
In 2020, Thompson published Why I Am Not A Buddhist, which argues against what he calls Buddhist exceptionalism, "the belief that Buddhism is superior to other religions...or that Buddhism isn't really a religion but rather is a kind of 'mind science,' therapy, philosophy, or a way of life based on meditation.