Infectious diseases caused by microbial pathogens (bacteria, virus, fungi, parasites) claim millions of deaths per year worldwide and have become a serious challenge to global human health in our century. Viral infections are particularly notable in this regard, not only because humankind is facing some of the deadliest viral pandemics in recent history, but also because the arsenal of drugs to combat the high levels of mutation, and hence the antigenic variability of (mostly RNA) viruses, is disturbingly scarce. Therefore, the search for new antivirals able to successfully fight infection with minimal or no adverse effects on the host is a pressing task. Traditionally, antiviral therapies have relied on relatively small-sized drugs acting as proteases, polymerases, integrase inhibitors, etc. In recent decades, novel approaches involving targeted delivery such as that achieved by peptide–drug conjugates (PDCs) have gained attention as alternative (pro)drugs for tackling viral diseases. Antiviral PDC therapeutics typically involve one or more small drug molecules conjugated to a cell-penetrating peptide (CPP) carrier either directly or through a linker. Such integration of two bioactive elements into a single molecular entity is primarily aimed at achieving improved bioavailability in conditions where conventional drugs are challenged, but may also turn up novel unexpected functionalities and applications. Advances in peptide medicinal chemistry have eased the way to antiviral PDCs, but challenges remain on the way to therapeutic success. In this paper, we review current antiviral CPP–drug conjugates (antiviral PDCs), with emphasis on the types of CPP and antiviral cargo. We integrate the conjugate and the chemical approaches most often applied to combine both entities. Additionally, we comment on various obstacles faced in the design of antiviral PDCs and on the future outlooks for this class of antiviral therapeutics.