The dynamics of protein binding pockets are crucial for their interaction specificity. Structural flexibility allows proteins to adapt to their individual molecular binding partners and facilitates the binding process. This implies the necessity to consider protein internal motion in determining and predicting binding properties and in designing new binders. Although accounting for protein dynamics presents a challenge for computational approaches, it expands the structural and physicochemical space for compound design and thus offers the prospect of improved binding specificity and selectivity. A cavity on the surface or in the interior of a protein that possesses suitable properties for binding a ligand is usually referred to as a binding pocket. The set of amino acid residues around a binding pocket determines its physicochemical characteristics and, together with its shape and location in a protein, defines its functionality. Residues outside the binding site can also have a long-range effect on the properties of the binding pocket. Cavities with similar functionalities are often conserved across protein families. For example, enzyme active sites are usually concave surfaces that present amino acid residues in a suitable configuration for binding low molecular weight compounds. Macromolecular binding pockets, on the other hand, are located on the protein surface and are often shallower. The mobility of proteins allows the opening, closing, and adaptation of binding pockets to regulate binding processes and specific protein functionalities. For example, channels and tunnels can exist permanently or transiently to transport compounds to and from a binding site. The influence of protein flexibility on binding pockets can vary from small changes to an already existent pocket to the formation of a completely new pocket. Here, we review recent developments in computational methods to detect and define binding pockets and to study pocket dynamics. We introduce five different classes of protein pocket dynamics: (1) appearance/disappearance of a subpocket in an existing pocket; (2) appearance/disappearance of an adjacent pocket on the protein surface in the direct vicinity of an already existing pocket; (3) pocket breathing, which may be caused by side-chain fluctuations or backbone or interdomain vibrational motion; (4) opening/closing of a channel or tunnel, connecting a pocket inside the protein with solvent, including lid motion; and (5) the appearance/disappearance of an allosteric pocket at a site on a protein distinct from an already existing pocket with binding of a ligand to the allosteric binding site affecting the original pocket. We suggest that the class of pocket dynamics, as well as the type and extent of protein motion affecting the binding pocket, should be factors considered in choosing the most appropriate computational approach to study a given binding pocket. Furthermore, we examine the relationship between pocket dynamics classes and induced fit, conformational selection, and gating models of ligand binding on binding kinetics and thermodynamics. We discuss the implications of protein binding pocket dynamics for drug design and conclude with potential future directions for computational analysis of protein binding pocket dynamics.