The concept of geroscience is that since ageing is the greatest risk factor for many diseases and conditions, targeting the ageing process itself will have the greatest impact on human health. Of the hallmarks of ageing, cellular senescence has emerged as a druggable therapeutic target for extending healthspan in model organisms. Cellular senescence is a cell state of irreversible proliferative arrest driven by different types of stress, including oncogene‐induced stress. Many senescent cells (SnCs) develop a senescent‐associated secretory phenotype (SASP) comprising pro‐inflammatory cytokines, chemokines, proteases, bioactive lipids, inhibitory molecules, extracellular vesicles, metabolites, lipids and other factors, able to promote chronic inflammation and tissue dysfunction. SnCs up‐regulate senescent cell anti‐apoptotic pathways (SCAPs) that prevent them from dying despite the accumulation of damage to DNA and other organelles. These SCAPs and other pathways altered in SnCs represent therapeutic targets for the development of senotherapeutic drugs that induce selective cell death of SnCs, specifically termed senolytics or suppress markers of senescence, in particular the SASP, termed senomorphics. Here, we review the current state of the development of senolytics and senomorphics for the treatment of age‐related diseases and disorders and extension of healthy longevity. In addition, the challenges of documenting senolytic and senomorphic activity in pre‐clinical models and the current state of the clinical application of the different senotherapeutics will be discussed.