The fundamental roles that peptides and proteins play in today's biology makes it almost indisputable that peptides were key players in the origin of life. Insofar as it is appropriate to extrapolate back from extant biology to the prebiotic world, one must acknowledge the critical importance that interconnected molecular networks, likely with peptides as key components, would have played in life's origin. In this review, we summarize chemical processes involving peptides that could have contributed to early chemical evolution, with an emphasis on molecular interactions between peptides and other classes of organic molecules. We first summarize mechanisms by which amino acids and similar building blocks could have been produced and elaborated into proto-peptides. Next, non-covalent interactions of peptides with other peptides as well as with nucleic acids, lipids, carbohydrates, metal ions, and aromatic molecules are discussed in relation to the possible roles of such interactions in chemical evolution of structure and function. Finally, we describe research involving structural alternatives to peptides and covalent adducts between amino acids/peptides and other classes of molecules. We propose that ample future breakthroughs in origin-of-life chemistry will stem from investigations of interconnected chemical systems in which synergistic interactions between different classes of molecules emerge.