The functional complexity of the central nervous system (CNS) is unparalleled in living organisms. Its nested cells, circuits and networks encode memories, move bodies and generate experiences. Neural tissues can be engineered to assemble model systems that recapitulate essential features of the CNS and to investigate neurodevelopment, delineate pathophysiology, improve regeneration and accelerate drug discovery. In this Review, we discuss essential structure–function relationships of the CNS and examine materials and design considerations, including composition, scale, complexity and maturation, of cell biology-based and engineering-based CNS models. We highlight region-specific CNS models that can emulate functions of the cerebral cortex, hippocampus, spinal cord, neural-X interfaces and other regions, and investigate a range of applications for CNS models, including fundamental and clinical research. We conclude with an outlook to future possibilities of CNS models, highlighting the engineering challenges that remain to be overcome.