The natural history of multiple sclerosis (MS) is highly heterogeneous. A subgroup of patients has what might be termed aggressive MS. These patients may have frequent, severe relapses with incomplete recovery and are at risk of developing greater and permanent disability at the earlier stages of the disease. Their therapeutic window of opportunity may be narrow, and while it is generally considered that they will benefit from starting early with a highly efficacious treatment, a unified definition of aggressive MS does not exist and data on its treatment are largely lacking. Based on discussions at an international focused workshop sponsored by the European Committee for Treatment and Research in Multiple Sclerosis (ECTRIMS), we review our current knowledge about treatment of individuals with aggressive MS. We analyse the available evidence, identify gaps in knowledge and suggest future research needed to fill those gaps. A companion paper details the difficulties in developing a consensus about what defines aggressive MS.