Cellular senescence represents a distinct cell fate characterized by replicative arrest in response to a host of extrinsic and intrinsic stresses. Senescence provides programming during development and wound healing, while limiting tumorigenesis. However, pathologic accumulation of senescent cells is implicated in a range of diseases and age-associated morbidities across organ systems. Senescent cells produce distinct paracrine and endocrine signals, causing local tissue dysfunction and exerting deleterious systemic effects. Senescent cell removal by apoptosis-inducing "senolytic" agents or therapies that inhibit the senescence-associated secretory phenotype, SASP inhibitors, have demonstrated benefit in both pre-clinical and clinical models of geriatric decline and chronic diseases, suggesting senescent cells represent a pharmacologic target for alleviating effects of fundamental aging processes. However, senescent cell populations are heterogeneous in form, function, tissue distribution, and even differ among species, possibly explaining issues of bench-to-bedside translation in current clinical trials. Here, we review features of senescent cells and strategies for targeting them, including immunologic approaches, as well as key intracellular signaling pathways. Additionally, we survey current senolytic therapies in human trials. Collectively, there is demand for research to develop targeted senotherapeutics that address the needs of the aging and chronically-ill.