To date, the leading causes of mortality and morbidity worldwide include viral infections, such as Ebola, influenza virus, acquired immunodeficiency syndrome (AIDS), severe acute respiratory syndrome (SARS) and recently COVID-19 disease, caused by the SARS-CoV-2 virus. Currently, we can count on a narrow range of antiviral drugs, especially older generation ones like ribavirin and interferon which are effective against viruses in vitro but can often be ineffective in patients. In addition to these, we have antiviral agents for the treatment of herpes virus, influenza virus, HIV and hepatitis virus. Recently, drugs used in the past especially against ebolavirus, such as remdesivir and favipiravir, have been considered for the treatment of COVID-19 disease. However, even if these drugs represent important tools against viral diseases, they are certainly not sufficient to defend us from the multitude of viruses present in the environment. This represents a huge problem, especially considering the unprecedented global threat due to the advancement of COVID-19, which represents a potential risk to the health and life of millions of people. The demand, therefore, for new and effective antiviral drugs is very high. This review focuses on three fundamental points: (1) presents the main threats to human health, reviewing the most widespread viral diseases in the world, thus describing the scenario caused by the disease in question each time and evaluating the specific therapeutic remedies currently available. (2) It comprehensively describes main phytochemical classes, in particular from plant foods, with proven antiviral activities, the viruses potentially treated with the described phytochemicals. (3) Consideration of the various applications of drug delivery systems in order to improve the bioavailability of these compounds or extracts. A PRISMA flow diagram was used for the inclusion of the works. Taking into consideration the recent dramatic events caused by COVID-19 pandemic, the cry of alarm that denounces critical need for new antiviral drugs is extremely strong. For these reasons, a continuous systematic exploration of plant foods and their phytochemicals is necessary for the development of new antiviral agents capable of saving lives and improving their well-being.