Current severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) vaccines, based on the ancestral Wuhan strain, were developed rapidly to meet the needs of a devastating global pandemic. People living with Human Immunodeficiency Virus (PLWH) have been designated as a priority group for SARS-CoV-2 vaccination in most regions and varying primary courses (two- or three-dose schedule) and additional boosters are recommended depending on current CD4+ T cell count and/or detectable HIV viraemia. From the current published data, licensed vaccines are safe for PLWH, and stimulate robust responses to vaccination in those well controlled on antiretroviral therapy and with high CD4+ T cell counts. Data on vaccine efficacy and immunogenicity remain, however, scarce in PLWH, especially in people with advanced disease. A greater concern is a potentially diminished immune response to the primary course and subsequent boosters, as well as an attenuated magnitude and durability of protective immune responses. A detailed understanding of the breadth and durability of humoral and T cell responses to vaccination, and the boosting effects of natural immunity to SARS-CoV-2, in more diverse populations of PLWH with a spectrum of HIV-related immunosuppression is therefore critical. This article summarizes focused studies of humoral and cellular responses to SARS-CoV-2 infection in PLWH and provides a comprehensive review of the emerging literature on SARS-CoV-2 vaccine responses. Emphasis is placed on the potential effect of HIV-related factors and presence of co-morbidities modulating responses to SARS-CoV-2 vaccination, and the remaining challenges informing the optimal vaccination strategy to elicit enduring responses against existing and emerging variants in PLWH.