The enteroviruses (EVs) of the Picornaviridae family are the most common viral pathogens known. Most EV infections are mild and self-limiting but manifestations can be severe in children and immunodeficient individuals. Antiviral development is actively pursued to benefit these high-risk patients and, given the alarming problem of antimicrobial drug resistance, antiviral drug resistance is a public-health concern. Picornavirus antivirals can be used off-label or as part of outbreak control measures. They may be used in the final stages of poliovirus eradication and to mitigate EV-A71 outbreaks. We review the potential emergence of drug-resistant strains and their impact on EV transmission and endemic circulation. We include non-picornavirus antivirals that inhibit EV replication, for example, ribavirin, a treatment for infection with HCV, and amantadine, a treatment for influenza A. They may have spurred resistance emergence in HCV or influenza A patients who are unknowingly coinfected with EV. The public-health challenge is always to find a balance between individual benefit and the long-term health of the larger population.