Nowadays, infectious diseases of bacterial and viral origins represent a serious medical problem worldwide. In fact, the development of antibiotic resistance is responsible for the emergence of bacterial strains that are refractory even to new classes of antibiotics. Furthermore, the recent COVID-19 pandemic suggests that new viruses can emerge and spread all over the world. The increase in infectious diseases depends on multiple factors, including malnutrition, massive migration of population from developing to industrialized areas, and alteration of the human microbiota. Alternative treatments to conventional antibiotics and antiviral drugs have intensively been explored. In this regard, plants and marine organisms represent an immense source of products, such as polyphenols, alkaloids, lanthipeptides, and terpenoids, which possess antibacterial and antiviral activities. Their main mechanisms of action involve modifications of bacterial cell membranes, with the formation of pores, the release of cellular content, and the inhibition of bacterial adherence to host cells, as well as of the efflux pump. Natural antivirals can interfere with viral replication and spreading, protecting the host with the enhanced production of interferon. Of note, these antivirals are not free of side effects, and their administration to humans needs more research in terms of safety. Preclinical research with natural antibacterial and antiviral compounds confirms their effects against bacteria and viruses, but there are still only a few clinical trials. Therefore, their full exploitation and more intensive clinical studies represent the next steps to be pursued in this area of medicine.