In-frame premature termination codons (PTCs) (also referred to as nonsense mutations) comprise ~10% of all disease-associated gene lesions. PTCs reduce gene expression in two ways. First, PTCs prematurely terminate translation of an mRNA, leading to the production of a truncated polypeptide that often lacks normal function and/or is unstable. Second, PTCs trigger degradation of an mRNA by activating nonsense-mediated mRNA decay (NMD), a cellular pathway that recognizes and degrades mRNAs containing a PTC. Thus, translation termination and NMD are putative therapeutic targets for the development of treatments for genetic diseases caused by PTCs. Over the past decade, significant progress has been made in the identification of compounds with the ability to suppress translation termination of PTCs (also referred to as readthrough). More recently, NMD inhibitors have also been explored as a way to enhance the efficiency of PTC suppression. Due to their relatively low threshold for correction, lysosomal storage diseases are a particularly relevant group of diseases to investigate the feasibility of nonsense suppression as a therapeutic approach. In this review, the current status of PTC suppression and NMD inhibition as potential treatments for lysosomal storage diseases will be discussed.