Inherited metabolic diseases (IMDs) belong to the group of rare diseases due to their low individual prevalence. Most of them are inherited in autosomal recessive fashion and represent good candidates for novel therapeutical strategies aimed at recovering partial enzyme function as they lack an effective treatment, and small levels of enzymatic activity have been shown to be associated with improved outcome and milder phenotypes. Recently, a novel therapeutic approach for genetic diseases has emerged, based on the ability of aminoglycosides and other compounds in allowing translation to proceed through a premature termination codon introduced by a nonsense mutation, which frequently constitute a significant fraction of the mutant alleles in a population. In this review we summarize the essentials of what is known as suppression therapy, the different compounds that have been identified by high-throughput screens or developed using a medicinal chemistry approach and the preclinical and clinical trials that are being conducted in general and in the field of IMDs in particular. Several IMDs have shown to be good models for evaluating readthrough compounds using patients’ cells carrying nonsense mutations, monitoring for an increase in functional recovery and/or enzyme activity. Overall, the positive results obtained indicate the feasibility of the approach for different diseases and although the levels of protein function reached are low, they may be enough to alleviate the consequences of the pathology. Nonsense suppression thus represents a potential therapy or supplementary treatment for a number of IMD patients encouraging further clinical trials with readthrough drugs with improved functionality and low toxicity.