The global public health threat of antimicrobial resistance has led the scientific community to highly engage into research on alternative strategies to the traditional small molecule therapeutics. Here, we review one of the most popular alternatives amongst basic and applied research scientists, synthetic antimicrobial peptides. The ease of peptide chemical synthesis combined with emerging engineering principles and potent broad-spectrum activity, including against multidrug-resistant strains, has motivated intense scientific focus on these compounds for the past decade. This global effort has resulted in significant advances in our understanding of peptide antimicrobial activity at the molecular scale. Recent evidence of molecular targets other than the microbial lipid membrane, and efforts towards consensus antimicrobial peptide motifs, have supported the rise of molecular engineering approaches and design tools, including machine learning. Beyond molecular concepts, supramolecular chemistry has been lately added to the debate; and helped unravel the impact of peptide self-assembly on activity, including on biofilms and secondary targets, while providing new directions in pharmaceutical formulation through taking advantage of peptide self-assembled nanostructures. We argue that these basic research advances constitute a solid basis for promising industry translation of rationally designed synthetic peptide antimicrobials, not only as novel drugs against multidrug-resistant strains but also as components of emerging antimicrobial biomaterials. This perspective is supported by recent developments of innovative peptide-based and peptide-carrier nanobiomaterials that we also review.