In the past few decades, driven by the increasing demands in the biomedical field aiming to cure neurological diseases and improve the quality of daily lives of the patients, researchers began to take advantage of the semiconductor technology to develop miniaturized and power-efficient chips for implantable applications. The emergence of the integrated circuits for neural prosthesis improves the treatment process of epilepsy, hearing loss, retinal damage, and other neurological diseases, which brings benefits to many patients. However, considering the safety and accuracy in the neural prosthesis process, there are many research directions. In the process of chip design, designers need to carefully analyze various parameters, and investigate different design techniques. This article presents the advances in neural recording and stimulation integrated circuits, including (1) a brief introduction of the basics of neural prosthesis circuits and the repair process in the bionic neural link, (2) a systematic introduction of the basic architecture and the latest technology of neural recording and stimulation integrated circuits, (3) a summary of the key issues of neural recording and stimulation integrated circuits, and (4) a discussion about the considerations of neural recording and stimulation circuit architecture selection and a discussion of future trends. The overview would help the designers to understand the latest performances in many aspects and to meet the design requirements better.