The complement cascade is an important arm of the immune system that plays a key role in protecting the central nervous system (CNS) from infection. Recently, it has also become clear that complement proteins have fundamental roles in the developing and aging CNS that are distinct from their roles in immunity. During neurodevelopment, complement signalling is involved in diverse processes including neural tube closure, neural progenitor proliferation and differentiation, neuronal migration, and synaptic pruning. In acute neurotrauma and ischamic brain injury, complement drives inflammation and neuronal death, but also neuroprotection and regeneration. In diseases of the aging CNS including dementias and motor neuron disease, chronic complement activation is associated with glial activation, and synapse and neuron loss. Proper regulation of complement is thus essential to allow for an appropriately developed CNS and prevention of excessive damage following neurotrauma or during neurodegeneration. This review provides a comprehensive overview of the evidence for functional roles of complement in brain formation, and its dysregulation during acute and chronic disease. We also provide working models for how complement can lead to neurodevelopmental disorders such as schizophrenia and autism, and either protect, or propagate neurodegenerative diseases including Alzheimer's disease and amyotrophic lateral sclerosis.