Engineered systems that can serve as chronically stable, high-performance electronic recording and stimulation interfaces to the brain and other parts of the nervous system, with cellular-level resolution across macroscopic areas, are of broad interest to the neuroscience and biomedical communities. Challenges remain in the development of biocompatible materials and the design of flexible implants for these purposes, where ulimate goals are for performance attributes approaching those of conventional wafer-based technologies and for operational timescales reaching the human lifespan. This Review summarizes recent advances in this field, with emphasis on active and passive constituent materials, design architectures and integration methods that support necessary levels of biocompatibility, electronic functionality, long-term stable operation in biofluids and reliability for use in vivo. Bioelectronic systems that enable multiplexed electrophysiological mapping across large areas at high spatiotemporal resolution are surveyed, with a particular focus on those with proven chronic stability in live animal models and scalability to thousands of channels over human-brain-scale dimensions. Research in materials science will continue to underpin progress in this field of study. This Review provides an overview of the advances in materials and device design that are enabling the realization of implantable electronic interfaces for long-term, multiplexed recording and stimulation of the brain and nervous system.