Several strategies have been developed to fight viral infections, not only in humans but also in animals and plants. Some of them are based on the development of efficient vaccines, to target the virus by developed antibodies, others focus on finding antiviral compounds with activities that inhibit selected virus replication steps. Currently, there is an increasing number of antiviral drugs on the market; however, some have unpleasant side effects, are toxic to cells, or the viruses quickly develop resistance to them. As the current situation shows, the combination of multiple antiviral strategies or the combination of the use of various compounds within one strategy is very important. The most desirable are combinations of drugs that inhibit different steps in the virus life cycle. This is an important issue especially for RNA viruses, which replicate their genomes using error-prone RNA polymerases and rapidly develop mutants resistant to applied antiviral compounds. Here, we focus on compounds targeting viral structural capsid proteins, thereby inhibiting virus assembly or disassembly, virus binding to cellular receptors, or acting by inhibiting other virus replication mechanisms. This review is an update of existing papers on a similar topic, by focusing on the most recent advances in the rapidly evolving research of compounds targeting capsid proteins of RNA viruses.