Myotonic dystrophy type 1 (DM1) is considered a progeroid disease (i.e., causing premature aging). This hypervariable disease affects multiple systems, such as the musculoskeletal, central nervous, gastrointestinal, and others. Despite advances in understanding the underlying pathogenic mechanism of DM1, numerous gaps persist in our understanding, hindering elucidation of the heterogeneity and severity of its symptoms. Accumulating evidence indicates that the toxic intracellular RNA accumulation associated with DM1 triggers cellular senescence. These cells are in a state of irreversible cell cycle arrest and secrete a cocktail of cytokines, referred to as a senescence-associated secretory phenotype (SASP), that can have harmful effects on neighboring cells and more broadly. We hypothesize that cellular senescence contributes to the pathophysiology of DM1, and clearance of senescent cells is a promising therapeutic approach for DM1. We will discuss the therapeutic potential of different senotherapeutic drugs, especially senolytics that eliminate senescent cells, and senomorphics that reduce SASP expression.