At present, much attention is paid to the use of antimicrobial peptides (AMPs) of natural and artificial origin to combat pathogens. AMPs have several points that determine their biological activity. We analyzed the structural properties of AMPs, as well as described their mechanism of action and impact on pathogenic bacteria and viruses. Recently published data on the development of new AMP drugs based on a combination of molecular design and genetic engineering approaches are presented. In this article, we have focused on information on the amyloidogenic properties of AMP. This review examines AMP development strategies from the perspective of the current high prevalence of antibiotic-resistant bacteria, and the potential prospects and challenges of using AMPs against infection caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). © 2020 by the authors. Licensee MDPI, Basel, Switzerland.