The COVID-19 pandemic, as well as the more general global increase in viral diseases, has led researchers to look to the plant kingdom as a potential source for antiviral compounds. Since ancient times, herbal medicines have been extensively applied in the treatment and prevention of various infectious diseases in different traditional systems. The purpose of this review is to highlight the potential antiviral activity of plant compounds as effective and reliable agents against viral infections, especially by viruses from the coronavirus group. Various antiviral mechanisms shown by crude plant extracts and plant-derived bioactive compounds are discussed. The understanding of the action mechanisms of complex plant extract and isolated plant-derived compounds will help pave the way towards the combat of this life-threatening disease. Further, molecular docking studies, in silico analyses of extracted compounds, and future prospects are included. The in vitro production of antiviral chemical compounds from plants using molecular pharming is also considered. Notably, hairy root cultures represent a promising and sustainable way to obtain a range of biologically active compounds that may be applied in the development of novel antiviral agents.