Networks of amyloid-like nanofibrils assembled from short peptide sequences have the ability to form scaffolds that can encapsulate clinically relevant stem cells encouraging their attachment, growth, and differentiation into various lineages which can be used in tissue engineering applications to treat a range of diseases and traumas. In this review, the author highlights a selection of important proof-of-principle papers that show how this class of self-assembled networks is highly suited to biomaterial scaffold development. The author highlights recent studies which have shown that these scaffolds can be used to promote cell and tissue regeneration both in vitro and in vivo. The author also presents some fundamental knowledge gaps which are preventing the widespread translation of such scaffolds. Finally, the author outlines a selection of studies that elucidate molecular assembly mechanisms and biophysical properties of amyloid-like peptide nanofibrils and suggests how studies like these might lead to the ability to generate nanofibril scaffolds with bespoke properties for tissue engineering.