Detecting and analysing protein cavities provides significant information about active sites for biological processes (e.g. protein–protein or protein–ligand binding) in molecular graphics and modelling. Using the three-dimensional (3D) structure of a given protein (i.e. atom types and their locations in 3D) as retrieved from a PDB (Protein Data Bank) file, it is now computationally viable to determine a description of these cavities. Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels and grooves on the surface of a given protein. In this work, we survey the literature on protein cavity computation and classify algorithmic approaches into three categories: evolution-based, energy-based and geometry-based. Our survey focuses on geometric algorithms, whose taxonomy is extended to include not only sphere-, grid- and tessellation-based methods, but also surface-based, hybrid geometric, consensus and time-varying methods. Finally, we detail those techniques that have been customized for GPU (graphics processing unit) computing.