This article evaluates the epidemiological evidence for a relationship between vaccination and neurological disease, specifically multiple sclerosis, Guillain–Barré syndrome and narcolepsy. The statistical methods used to test vaccine safety hypotheses are described and the merits of different study designs evaluated; these include the cohort, case-control, case-coverage and the self-controlled case-series methods. For multiple sclerosis, the evidence does not support the hypothesized relationship with hepatitis B vaccine. For Guillain−Barré syndrome, the evidence suggests a small elevated risk after influenza vaccines, though considerably lower than after natural influenza infection, with no elevated risk after human papilloma virus vaccine. For narcolepsy, there is strong evidence of a causal association with one adjuvanted vaccine used in the 2009/10 influenza pandemic. Rapid investigation of vaccine safety concerns, however biologically implausible, is essential to maintain public and professional confidence in vaccination programmes.