Four body composition phenotypes exist in older adults: normal, sarcopenic, obese, and a combination of sarcopenic and obese. There is no consensus, however, on the definitions and classifications of these phenotypes and their etiology and consequences continue to be debated. The lack of standard definitions, particularly for sarcopenia and sarcopenic obesity, creates challenges for determining prevalence across different populations. The etiology of these phenotypes is multifactorial with complex covariate relationships. This review focuses on the current literature addressing the classification, prevalence, etiology, and correlates of sarcopenia, obesity, and the combination of sarcopenia and obesity, referred to as sarcopenic obesity.