Peptides and proteins, two important classes of biomacromolecules, play important roles in the biopharmaceuticals field. As compared with traditional drugs based on small molecules, peptide- and protein-based drugs offer several advantages, although most cannot traverse the cell membrane, a natural barrier that prevents biomacromolecules from directly entering cells. However, drug delivery via cell-penetrating peptides (CPPs) is increasingly replacing traditional approaches that mediate biomacromolecular cellular uptake, due to CPPs’ superior safety and efficiency as drug delivery vehicles. In this review, we describe the discovery of CPPs, recent developments in CPP design, and recent advances in CPP applications for enhanced cellular delivery of peptide- and protein-based drugs. First, we discuss the discovery of natural CPPs in snake, bee, and spider venom. Second, we describe several synthetic types of CPPs, such as cyclic CPPs, glycosylated CPPs, and D-form CPPs. Finally, we summarize and discuss cell membrane permeability characteristics and therapeutic applications of different CPPs when used as vehicles to deliver peptides and proteins to cells, as assessed using various preclinical disease models. Ultimately, this review provides an overview of recent advances in CPP development with relevance to applications related to the therapeutic delivery of biomacromolecular drugs to alleviate diverse diseases.