Serious symptomatic SARS-CoV-2 infection and COVID-19 complications are particular concerns for people with multiple sclerosis, especially those receiving immunosuppressants or immunomodulators. Studies have aimed to identify individuals with multiple sclerosis who are at high risk for SARS-CoV-2 infection, to analyse the interplay between SARS-CoV-2 and multiple sclerosis and to evaluate immunological responses to SARS-CoV-2 infection and vaccines. The emergence of evolving dominant SARS-CoV-2 variants, a range of available vaccines, and novel therapeutic approaches requires that clinical neurologists be regularly updated with the latest information. Unresolved issues include optimisation of vaccination strategies to enhance vaccine efficacy and the management of patients who do not show seroconversion post vaccination. Tailored vaccination has the potential to improve patient care, and future studies should focus on evaluating novel therapies and preventive measures while constantly updating our knowledge of potential SARS-CoV-2 variants, in preparation for future outbreaks or pandemics.