In the era of a growing global threat of antibiotic resistance, antimicrobial peptides (AMPs) are considered to be representatives of a new generation of drugs for a treatment of various infectious diseases. In this review, AMPs are discussed as an alternative to traditional antibiotics, many of which have already lost or have a decreased effectiveness against a number of critically important pathogenic microorganisms. Recent outbreaks of secondary infections during the COVID-19 pandemic have increased the interest in AMPs due to an acute shortage of effective agents against bacterial and fungal infections. The review summarizes current data on clinical studies of AMPs, emphasizes the importance of a search for and investigation of new AMPs, and describes various AMP-based therapeutic agents for which clinical trials are continuing or have already finished.