Biologic immunotherapies have transformed the treatment landscape of multiple sclerosis. Such therapies include recombinant proteins (interferon beta), as well as monoclonal antibodies (natalizumab, alemtuzumab, daclizumab, rituximab and ocrelizumab). Monoclonal antibodies show particular efficacy in the treatment of the inflammatory phase of multiple sclerosis. However, the immunological perturbations caused by biologic therapies are associated with significant immunological adverse reactions. These include development of neutralising immunogenicity, secondary immunodeficiency and secondary autoimmunity. These complications can affect the balance of risks and benefits of biologic agents, and 2018 saw the withdrawal from the market of daclizumab, an anti-CD25 monoclonal antibody, due to concerns about the development of severe, unpredictable autoimmunity. Here we review established and emerging risks associated with multiple sclerosis biologic agents, with an emphasis on their immunological adverse effects. We also discuss the specific challenges that multiple sclerosis biologics pose to drug safety systems, and the potential for improvements in safety frameworks.