The complement system consists of a network of plasma and membrane proteins that modulate tissue homeostasis and contribute to immune surveillance by interacting with the innate and adaptive immune systems. Dysregulation, impairment or inadvertent activation of complement components contribute to the pathogenesis of some autoimmune neurological disorders and could even contribute to neurodegenerative diseases. In this Review, we summarize current knowledge about the main functions of the complement pathways and the involvement of complement in neurological disorders. We describe the complex network of complement proteins that target muscle, the neuromuscular junction, peripheral nerves, the spinal cord or the brain and discuss the autoimmune mechanisms of complement-mediated myopathies, myasthenia, peripheral neuropathies, neuromyelitis and other CNS disorders. We also consider the emerging role of complement in some neurodegenerative diseases, such as Alzheimer disease, amyotrophic lateral sclerosis and even schizophrenia. Finally, we provide an overview of the latest complement-targeted immunotherapies including monoclonal antibodies, fusion proteins and peptidomimetics that have been approved, that are undergoing phase I-III clinical trials or that show promise for the treatment of neurological conditions that respond poorly to existing immunotherapies.