Disease-modifying drugs (DMDs) for relapsing-remitting multiple sclerosis (RRMS) are only partly effective -- breakthrough disease commonly occurs despite treatment. Breakthrough disease is predictive of continued disease activity and a poor prognosis. Availability of several DMDs offers the possibility of tailoring treatment to individual patients with RRMS and altering treatment in patients with breakthrough disease. However, no biological or imaging markers have been validated to guide initial treatment, markers of individual responsiveness to DMDs are scarce, and there is no class 1 evidence to guide alternative therapy in patients with breakthrough disease. In this Review, we discuss proposed strategies to monitor patients with RRMS being treated with DMDs, outline approaches to identifying therapeutic response in individual patients, review MRI and biological markers of treatment response, and summarise the role of antibodies in biological therapies. We also outline possible strategies for the management of patients with breakthrough disease and highlight areas in which research is needed.