The Fatty Acid Amide Hydrolase (FAAH) enzyme is a membrane-bound serine hydrolase responsible for the deactivating hydrolysis of a family of naturally occurring fatty acid amides. FAAH is a critical enzyme of the endocannabinoid system, being mainly responsible for regulating the level of its main cannabinoid substrate anandamide. For this reason, pharmacological inhibition of FAAH, which increases the level of endogenous anandamide, is a promising strategy to cure a variety of diseases including pain, inflammation, and cancer. Much structural, mutagenesis, and kinetic data on FAAH has been generated over the last couple of decades. This has prompted several informative computational investigations to elucidate, at the atomic-level, mechanistic details on catalysis and inhibition of this pharmaceutically relevant enzyme. Here, we review how these computational studies - based on classical molecular dynamics, full quantum mechanics, and hybrid QM/MM methods - have clarified the binding and reactivity of some relevant substrates and inhibitors of FAAH. We also discuss the experimental implications of these computational insights, which have provided a thoughtful elucidation of the complex physical and chemical steps of the enzymatic mechanism of FAAH. Finally, we discuss how computations have been helpful for building structure activity relationships of potent FAAH inhibitors. (C) 2014 Elsevier Masson SAS. All rights reserved.