Protein-protein interactions (PPIs) are fundamental to a variety of biological processes, but targeting them with small molecules is challenging because of their large and complex interaction interfaces. However, peptides have emerged as highly promising modulators of PPIs, because they can bind to protein surfaces with high affinity and specificity. Nonetheless, computational peptide design remains difficult, hindered by the intrinsic flexibility of peptides and the substantial computational resources required. Recent advances in artificial intelligence (AI) are paving new paths for peptide-based drug design. In this review, we explore the advanced deep generative models for designing target-specific peptide binders, highlight key challenges, and offer insights into the future direction of this rapidly evolving field.