The study of the SUP45 and SUP35 genes of yeast Saccharomyces cerevisiae in the laboratory of Physiological Genetics of St. Petersburg State University began in 1964 when the first omnipotent nonsense suppressor mutations were obtained. During the following 55 years, a lot of information about these genes has been gained through the research efforts of various laboratories. Now we know that SUP45 and SUP35 encode translation termination factors eRF1 and eRF3, respectively. Both genes are essential, and sup45 and sup35 mutations lead not only to impaired translation but also to multiple pleiotropic effects. The aim of this review is to summarize known data about suppressor mutations in SUP45 or SUP35 genes.