Nonsense mutations that generate a premature termination codon (PTC) can induce both the accelerated degradation of mutated mRNA compared with the wild type version of the mRNA or the production of a truncated protein. One of the considered therapeutic strategies to bypass PTCs is their “readthrough” based on small-molecule drugs. These molecules promote the incorporation of a near-cognate tRNA at the PTC position through the native polypeptide chain. In this review, we detailed the various existing strategies organized according to pharmacological molecule types through their different mechanisms. The positive results that followed readthrough molecule testing in multiple neuromuscular disorder models indicate the potential of this approach in peripheral neuropathies.