Inspired by self-assembling peptides found in native proteins, deliberately designed engineered peptides have shown outstanding biocompatibility, biodegradability, and extracellular matrix-mimicking microenvironments. Assembly of the peptides can be triggered by external stimuli, such as electrolytes, temperature, and pH. The formation of nanostructures and subsequent nanocomposite materials often occur under physiological conditions. The respective properties of side chains in each amino acids provide numerous sites for chemical modification and conjugation choices of the peptides, enabling various resulting supramolecular nanostructures and hydrogels with adjustable mechanical and physicochemical properties. Moreover, additional functionalities can be easily induced into the hydrogels, including shear-thinning, bioactivity, self-healing, and shape memory. It further broaden the scope of application of self-assemble peptide materials. This review outlines designs of self-assembly peptide (β-sheet, α-helix, collagen-like peptides, elastin-like polypeptides, and peptide amphiphiles) with potential additional functionalities and their biomedical applications in bioprinting, tissue engineering, and drug delivery.