Requirements and recent advances in research on organic neuroelectronics are outlined herein. Neuroelectronics such as neural interfaces and neuroprosthetics provide a promising approach to diagnose and treat neurological diseases. However, the current neural interfaces are rigid and not biocompatible, so they induce an immune response and deterioration of neural signal transmission. Organic materials are promising candidates for neural interfaces, due to their mechanical softness, excellent electrochemical properties, and biocompatibility. Also, organic nervetronics, which mimics functional properties of the biological nerve system, is being developed to overcome the limitations of the complex and energy-consuming conventional neuroprosthetics that limit long-term implantation and daily-life usage. Examples of organic materials for neural interfaces and neural signal recordings are reviewed, recent advances of organic nervetronics that use organic artificial synapses are highlighted, and then further requirements for neuroprosthetics are discussed. Finally, the future challenges that must be overcome to achieve ideal organic neuroelectronics for next-generation neuroprosthetics are discussed.