α-Amino acids are easily accessible through abiotic processes and were likely present before the emergence of life. However, the role they could have played in the process remains uncertain. Chemical pathways that could have brought about features of self-organization in a peptide world are considered in this review and discussed in relation with their possible contribution to the origin of life. An overall scheme is proposed with an emphasis on possibilities that may have led to dynamically stable far from equilibrium states. This analysis defines new lines of investigation towards a better understanding of the contribution of the systems chemistry of amino acids and peptides to the emergence of life.