Peptides hold great promise as novel medicinal and biologic agents, and computational methods can help unlock that promise. In particular, structure-based peptide design can be used to identify and optimize peptide ligands. Successful structure-based design, in turn, requires accurate and fast methods for predicting protein-peptide binding affinities. Here, we review the development of such methods, emphasizing structure-based methods that assume rigid-body association and the single-structure approximation. We also briefly review recent applications of computational free energy prediction methods to enable and guide novel peptide drug and biomarker discovery. We close the review with a brief perspective on the future of computational, structure-based protein-peptide binding affinity prediction.