The SARS-CoV-2 pandemic has raised particular concern for people with Multiple Sclerosis, as these people are believed to be at increased risk of infection, especially those being treated with disease-modifying therapies. Therefore, the objective of this review was to describe how COVID-19 affects people who suffer from Multiple Sclerosis, evaluating the risk they have of suffering an infection by this virus, according to the therapy to which they are subjected as well as the immune response of these patients both to infection and vaccines and the neurological consequences that the virus can have in the long term. The results regarding the increased risk of infection due to treatment are contradictory. B-cell depletion therapies may cause patients to have a lower probability of generating a detectable neutralizing antibody titer. However, more studies are needed to help understand how this virus works, paying special attention to long COVID and the neurological symptoms that it causes.