Nowadays, machine learning and deep learning approaches are widely utilized for generative chemistry and computer-aided drug design and discovery such as de novo peptide and protein design, where target-specific peptide-based/protein-based therapeutics have been suggested to cause fewer adverse effects than the traditional small-molecule drugs. In light of current advancements in deep learning techniques, generative adversarial network (GAN) algorithms are being leveraged to a wide variety of applications in the process of generative chemistry and computer-aided drug design and discovery. In this review, we focus on the up-to-date developments for de novo peptide and protein design research using GAN algorithms in the interdisciplinary fields of generative chemistry, machine learning, deep learning, and computer-aided drug design and discovery. First, we present various studies that investigate GAN algorithms to fulfill the task of de novo peptide and protein design in the drug development pipeline. In addition, we summarize the drawbacks with respect to the previous studies in de novo peptide and protein design using GAN algorithms. Finally, we depict a discussion of open challenges and emerging problems for future research.