Cystic fibrosis (CF) is a monogenic autosomal recessive disorder. The clinical manifestations of the disease are caused by ∼2,000 mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) protein. It is unlikely that any one approach will be efficient in correcting all defects. The recent approvals of ivacaftor, lumacaftor/ivacaftor and elexacaftor/tezacaftor/ivacaftor represent the genesis of a new era of precision combination medicine for the CF patient population. In this review, we discuss targeted translational readthrough approaches as mono and combination therapies for CFTR nonsense mutations. We examine the current status of efficacy of translational readthrough/nonsense suppression therapies and their limitations, including non-native amino acid incorporation at PTCs and nonsense-mediated mRNA decay (NMD), along with approaches to tackle these limitations. We further elaborate on combining various therapies such as readthrough agents, NMD inhibitors, and corrector/potentiators to improve the efficacy and safety of suppression therapy. These mutation specific strategies that are directed towards the basic CF defects should positively impact CF patients bearing nonsense mutations.