Neural interfaces are connections that enable two-way exchange of information with the nervous system. These connections can occur at multiple levels, including with peripheral nerves, with the spinal cord, or with the brain; in many instances, fundamental biophysical and biological challenges are shared across these levels. We review these challenges, including selectivity, stability, resolution versus invasiveness, implant-induced injury, and the host-interface response. Subsequently, we review the engineered solutions to these challenges, including electrode designs and geometry, stimulation waveforms, materials, and surface modifications. Finally, we consider emerging opportunities to improve neural interfaces, including cellular-level silicon to neuron connections, optical stimulation, and approaches to control inflammation. Overcoming the biophysical and biological challenges will enable effective high-density neural interfaces for stimulation and recording.