Coronaviruses are dangerous human and animal pathogens. The newly identified coronavirus SARS-CoV-2 is the causative agent of COVID-19 outbreak, which is a real threat to human health and life. The world has been struggling with this epidemic for about a year, yet there are still no targeted drugs and effective treatments are very limited. Due to the long process of developing new drugs, reposition of existing ones is one of the best ways to deal with an epidemic of emergency infectious diseases. Among the existing drugs there are candidates which are potentially able to inhibit the SARS-CoV-2 replication, and thus infection with the virus. Some therapeutics target several proteins, and many diseases share molecular paths. In such cases, the use of existing pharmaceuticals for more than one purposes can reduce the time needed to design new drugs. The aim of this review was to analyse the key targets of viral infection and potential drugs acting on them, as well as to discuss various strategies and therapeutic approaches, including the possible use of natural products. We highlight the approach based on increasing the involvement of human deaminases, particularly APOBEC deaminases in editing of SARS-CoV-2 RNA. This can reduce the cytosine content in the viral genome leading to the loss of its integrity. We also indicate the nucleic acid technologies as potential approaches for COVID-19 treatment. Among numerous promising natural products, we point out curcumin and cannabidiol as good candidates for being anti-SARS-CoV-2 agents.