Obesity is an independent risk factor for severe COVID-19, yet there remains a lack of consensus on the mechanisms underlying this relationship. A hypothesis that has garnered considerable attention suggests that SARS-CoV-2 disrupts adipose tissue function, either through direct infection or by indirect mechanisms. Indeed, recent reports have begun to shed some light on the important role that the adipose tissue plays during the acute phase of infection, as well as mediating long-term sequelae. In this review, we examine the evidence of extrapulmonary dissemination of SARS-CoV-2 to the adipose tissue. We discuss the mechanisms, acute and long-term implications, and possible management strategies to limit or ameliorate severe disease and long-term metabolic disturbances.