Nonsense suppression therapy encompasses approaches aimed at suppressing translation termination at in-frame premature termination codons (PTCs, also known as nonsense mutations) to restore deficient protein function. In this review, we examine the current status of PTC suppression as a therapy for genetic diseases caused by nonsense mutations. We discuss what is currently known about the mechanism of PTC suppression as well as therapeutic approaches under development to suppress PTCs. The approaches considered include readthrough drugs, suppressor tRNAs, PTC pseudouridylation, and inhibition of nonsense-mediated mRNA decay. We also discuss the barriers that currently limit the clinical application of nonsense suppression therapy and suggest how some of these difficulties may be overcome. Finally, we consider how PTC suppression may play a role in the clinical treatment of genetic diseases caused by nonsense mutations.