Antimicrobial peptides (AMPs) are naturally occurring macromolecules made of amino acids that are potent broad-spectrum antibiotics with potential as novel therapeutic agents. This review aims to summarize the fundamental principles concerning the structure and mechanism of action of these AMPs, in order to guide the design of polymeric analogues that organic chemistry can generate. Among those simplified analogues, this review particularly focuses on those made of amino acids called polypeptide polymers: they are showing great potential by providing one of the best biomimetic and bioactive structures for further biomaterials science applications.