The human complement system is an effector of innate and adaptive humoral immunity. The system comprises soluble membrane-bound proteins (opsonins) that act collectively to recognize pathogens and non-self material and subsequently initiate opsonization and phagocytosis or lysis of pathogens. The proteolytic fragments that derive from complement activation can be targeted by white blood cells and endothelial cells, leading to extravasation and migration of immune cells at the sites of inflammation. Other physiological functions of complement include timely removal of altered and senescent self, tissue remodelling, cell lysis, chemotaxis, opsonization, inflammation and immune cell stimulation 1-4. Complement activation products link the innate and adaptive immune systems by acting directly on receptors on T cells and B cells or by modulating dendritic cell functions 5-8. Disruption of the delicate coordination required for complement activation and control is fundamental in the pathogenic mechanism of several autoimmune neurological disorders, and is even emerging as a contributor in some neurodegenerative diseases. As a result, interest is increasing in targeting complement as a therapeutic approach to prevent ongoing tissue destruction in several difficult-to-treat neurological diseases. In this Review, we provide an overview of the main components of the initial complement activation pathways, the lytic pathway and the factors associated with inappropriate complement activation or control in disease initiation and progression. We consider the role of complement in the tissue destruction that is responsible for the genesis of the most common autoimmune neurological diseases, including complement-mediated myopathies, myasthenia gravis, neuropathies and CNS disorders. We also discuss the role of complement in some neurodegenerative disorders, including Alzheimer disease (AD), amyotrophic lateral sclerosis (ALS), Huntington disease, traumatic brain injury and even schizophrenia. Finally, we discuss emerging complement-targeted therapies, such as monoclonal antibodies, fusion proteins and cyclic peptides, that inhibit the functions of individual complement proteins, especially therapies that disrupt the lytic pathway. Some of these therapeutic agents have been approved or are being tested in phase I-III clinical trials and promise to change the therapeutic armamentarium for treatment of neurological conditions that respond poorly to existing immunotherapies.