Peptides are important signaling modules, acting both as individual hormones and as parts of larger molecules, mediating their protein-protein interactions. Many peptidic and peptidomimetic drugs have reached the marketplace and opportunities for peptide-based drug discovery are on the rise. pH-dependent behavior of peptides is well documented in the context of misfolding diseases and peptide translocation. Changes in the protonation states of peptide residues often have a crucial effect on a peptide's structure, dynamics and function, which may be exploited for biotechnological applications. The current review surveys the increasing levels of sophistication in the treatment of protonation states in computational studies involving peptides. Specifically we describe I) the common practice of assigning a single protonation state and using it throughout the dynamic simulation, II) approaches that consider multiple protonation states and compare computed observables to experimental ones, III) constant pH molecular dynamics methods that couple changes in protonation states with conformational dynamics "on the fly". Applications of conformational dynamics treatment of peptides in the context of binding, folding and interactions with the membrane are presented, illustrating the growing body of work in this field and highlighting the importance of careful handling of protonation states of peptidic residues.