Deep learning tools, especially deep generative models (DGMs), provide opportunities to accelerate and simplify the design of drugs. As drug candidates, peptides are superior to other biomolecules because they combine potency, selectivity, and low toxicity. This review examines the fundamental aspects of current DGMs for designing therapeutic peptide sequences. First, relevant databases in this field are introduced. Next, the current situation of data representation and where it can be optimized are discussed. Then, after introducing the basic principles and variants of diverse DGM algorithms, the applications of these methods to design and optimize peptides are stated. Finally, we present several challenges to devising a powerful model that can meet the requirements of learning the different biological properties of peptides, as well as future research directions to address these challenges.