Proteins are fundamentally the most important macromolecules for biochemical, mechanical, and structural functions in living organisms. Therefore, they provide us with diverse structural building blocks for constructing various types of biomaterials, including an important class of such materials, hydrogels. Since natural peptides and proteins are biocompatible and biodegradable, they have features advantageous for their use as the building blocks of hydrogels for biomedical applications. They display constitutional and mechanical similarities with the native extracellular matrix (ECM), and can be easily bio-functionalized via genetic and chemical engineering with features such as bio-recognition, specific stimulus-reactivity, and controlled degradation. This review aims to give an overview of hydrogels made up of recombinant proteins or synthetic peptides as the structural elements building the polymer network. A wide variety of hydrogels composed of protein or peptide building blocks with different origins and compositions - including β-hairpin peptides, α-helical coiled coil peptides, elastin-like peptides, silk fibroin, and resilin - have been designed to date. In this review, the structures and characteristics of these natural proteins and peptides, with each of their gelation mechanisms, and the physical, chemical, and mechanical properties as well as biocompatibility of the resulting hydrogels are described. In addition, this review discusses the potential of using protein- or peptide-based hydrogels in the field of biomedical sciences, especially tissue engineering.