Immunoediting is an important concept in oncology, delineating the mechanisms through which tumors are selected for resistance to immune-mediated elimination. The recent emergence of immunotherapies, such as checkpoint inhibitors, as pillars of cancer therapy has intensified interest in immunoediting as a constraint limiting the efficacy of these approaches. Immunoediting manifests at a number of levels for different cancers, for example through the establishment of immunosuppressive microenvironments within solid tumors. Of particular interest to the current review, selection also occurs at the cellular level; and recent studies have revealed novel mechanisms by which tumor cells acquire intrinsic resistance to immune recognition and elimination. While the selection of escape mutations in viral epitopes by HIV-specific T cells, which is a hallmark of chronic HIV infection, can be considered a form of immunoediting, few studies have considered the possibility that HIV-infected cells themselves may parallel tumors in having differential intrinsic susceptibilities to immune-mediated elimination. Such selection, on the level of an infected cell, may not play a significant role in untreated HIV, where infection is propagated by high levels of cell-free virus produced by cells that quickly succumb to viral cytopathicity. However, it may play an unappreciated role in individuals treated with effective antiretroviral therapy where viral replication is abrogated. In this context, an "HIV reservoir" persists, comprising long-lived infected cells which undergo extensive and dynamic clonal expansion. The ability of these cells to persist in infected individuals has generally been attributed to viral latency, thought to render them invisible to immune recognition, and/or to their compartmentalization in anatomical sites that are poorly accessible to immune effectors. Recent data from studies have led us to propose that reservoir-harboring cells may additionally have been selected for intrinsic resistance to CD8 T cells, limiting their elimination even in the context of antigen expression. Here, we draw on knowledge from tumor immunoediting to discuss potential mechanisms by which clones of HIV reservoir-harboring cells may resist elimination by CD8 T cells. The establishment of such parallels may provide a premise for testing therapeutics designed to sensitize tumor cells to immune-mediated elimination as novel approaches aimed at curing HIV infection.