Poor responses to medical care and the failure of pharmacological treatment for many high-frequency diseases, such as cancer and viral infections, have been widely documented. In this context, numerous metal-based substances, including cisplatin, auranofin, various gold metallodrugs, and ruthenium complexes, are under study as possible anticancer and antiviral agents. The two Ru(III) and Ru(II) complexes, namely, BOLD-100 and RAPTA-C, are presently being studied in a clinical trial and preclinical studies evaluation, respectively, as anticancer agents. Interestingly, BOLD-100 has also recently demonstrated antiviral activity against SARS-CoV-2, which is the virus responsible for the COVID-19 pandemic. Over the last years, much effort has been dedicated to discovering new dual anticancer–antiviral agents. Ru-based complexes could be very suitable in this respect. Thus, this review focuses on the most recent studies regarding newly synthesized Ru(II) complexes for use as anticancer and/or antiviral agents.