About 11% of all human disease-associated gene lesions are nonsense mutations, resulting in the introduction of an in-frame premature translation-termination codon (PTC) into the protein-coding gene sequence. When translated, PTC-containing mRNAs originate truncated and often dysfunctional proteins that might be non-functional or have gain-of-function or dominant-negative effects. Therapeutic strategies aimed at suppressing PTCs to restore deficient protein function-the so-called nonsense suppression (or PTC readthrough) therapies-have the potential to provide a therapeutic benefit for many patients and in a broad range of genetic disorders, including cancer. These therapeutic approaches comprise the use of translational readthrough-inducing compounds that make the translational machinery recode an in-frame PTC into a sense codon. However, most of the mRNAs carrying a PTC can be rapidly degraded by the surveillance mechanism of nonsense-mediated decay (NMD), thus decreasing the levels of PTC-containing mRNAs in the cell and their availability for PTC readthrough. Accordingly, the use of NMD inhibitors, or readthrough-compound potentiators, may enhance the efficiency of PTC suppression. Here, we review the mechanisms of PTC readthrough and their regulation, as well as the recent advances in the development of novel approaches for PTC suppression, and their role in personalized medicine.