The self-assembly of helical peptides and information transfer through autocatalysis and cross-catalysis are the foundation of peptide-based molecular evolution models. Many fundamental properties of living systems, such as environmental sensitivity, chiroselectivity, cross-catalysis, dynamic error correction and conditional selection, are exhibited by various self-replicating peptide systems. Recently, advances have been made in the design of peptide systems with autocatalytic and cross-catalytic properties.