The γ-secretase complex is composed of four membrane protein subunits, including presenilin as the catalytic component with aspartyl protease activity. The enzyme cleaves within the transmembrane domain of >70 different type I integral membrane proteins and has been dubbed "the proteasome of the membrane". The most studied substrates include the Notch family of receptors, involved in cell differentiation, and the amyloid precursor protein (APP), involved in the pathogenesis of Alzheimer's disease. A central mechanistic question is how γ-secretase recognizes helical transmembrane substrates and carries out processive proteolysis. Recent findings addressing substrate recognition and processing will be discussed, including the role of protease subunit nicastrin as a gatekeeper, the effects of Alzheimer-causing mutations in presenilin on processive proteolysis of APP, and evidence that three pockets in the active site (S1', S2', and S3') determine carboxypeptidase cleavage of substrate in intervals of three residues. This article is part of a Special Issue entitled: Molecular biophysics of membranes and membrane proteins. Copyright © 2019 Elsevier B.V. All rights reserved.