A primary obstacle to curing HIV infection is the early establishment of long-lived viral reservoirs from which infection rebounds if antiretroviral therapy (ART) is interrupted. There is currently considerable effort directed to devising strategies to eliminate or greatly reduce these reservoirs so it would be possible to discontinue ART for extended or indefinite periods of time, referred to as a functional cure. To date, these strategies have largely been assessed by monitoring changes in T cell HIV reservoirs from peripheral blood (PB), but the lymphoid tissues (LT) are the major tissue compartments where latently and persistently infected cells reside and infectious virus persists on the follicular dendritic cell network (FDCn) in lymphoid follicles. Because HIV is primarily a disease of lymphoid tissues, a detailed understanding of HIV reservoir establishment and persistence is particularly difficult to study in humans but can be readily studied in SIV nonhuman primate (NHP) models. These NHP models have been invaluable in understanding the timing of viral seeding, viral dynamics and compartmentalization, and cell populations involved in viral persistence within LTs. These studies have highlighted B cell follicles in viral persistence both before and during ART, with infected TFH cells and viral particles bound to the FDCn as potentially important cells harboring infectious virus. Novel strategies to purge virus from these tissues may be hindered by the pathologic damage to these immune organs induced by persistent chronic inflammation and immune activation, which leads to a profound impairment of normal lymph node function. Adjunctive strategies to reverse LT damage will likely need to be considered to realize the full potential of HIV cure therapeutic approaches, which will need full access to these important immune organs where most HIV reservoirs reside.