The current COVID-19 epidemic is both a health and societal issue; therefore, groups historically excluded and marginalised in terms of healthcare will suffer if COVID-19 vaccines, tests, and treatments are to be delivered equitably. This rapid review is exploring the social and cultural challenges related to the roll-out, distribution, and access of COVID-19 vaccines, tests, and treatments. It highlights how these challenges impact certain marginalised groups. Case studies are taken from sub-Saharan Africa (the Democratic Republic of Congo, South Africa), with some focus on South East Asia (Indonesia, India) as they have different at-risk groups. Lessons on this issue can be learned from previous pandemics and vaccine roll-out in low- and mid-income countries (LMICs). Key points to highlight include successful COVID-19 vaccine roll-out will only be achieved by ensuring effective community engagement, building local vaccine acceptability and confidence, and overcoming cultural, socio-economic, and political barriers that lead to mistrust and hinder uptake of vaccines. However, the literature notes that a lot of lessons learned about roll-out involve communication – including that the government should under-promise what it can do and then over-deliver. Any campaign must aim to create trust, and involve local communities in planning processes.