The bioavailability, release, and stability of pharmaceuticals under physicochemical conditions is the major cause of drug candidates failing during their clinical trials. Therefore, extensive efforts have been invested in the development of novel drug delivery systems that are able to transport drugs to a desired site and improve bioavailability. Hydrogels, and peptide hydrogels in particular, have been extensively investigated due to their excellent biocompatibility and biodegradability properties. However, peptide hydrogels often have weak mechanical strength, which limits their therapeutic efficacy. Therefore, a number of methods for improving their rheological properties have been established. This review will cover the broad area of drug delivery, focusing on the recent developments in this research field. We will discuss the variety of different types of nanocarrier drug delivery systems and then, more specifically, the significance and perspectives of peptide-based hydrogels. In particular, the interplay of intermolecular forces that govern the self-assembly of peptide hydrogels, progress made in understanding the distinct morphologies of hydrogels, and applications of non-canonical amino acids in hydrogel design will be discussed in more detail.