Abstract: Neurodynamics is a foundational branch of dynamics and control, which belongs to the international frontier of the interdisciplinary field of mechanics, brain science and intelligence science. Based on the basic theories and methods of dynamics and control, the study of neurodynamics mainly focuses on establishing reasonable models to explore the mechanisms of electrophysiological dynamic behaviors of nervous system and brain cognitive functions. In recent years, scholars at home and abroad have obtained remarkable achievements in the foundational research of neurodynamics, including the in-depth study of the dynamical behavior of neurons and neural networks, the modeling and analysis of different functional structures of the brain, and the network dynamics modeling and control of brain regions associated with nervous disease. In this paper, we firstly overviewed elaborately the recent advancements in the field of neurodynamics. Especially, development history for advancement of neural modeling is exhibited. Then, by analyzing the research outcomes of biological neural networks and their dynamics, some thoughts and prospects for future research are put forward. It is expected that neurodynamics will contribute to the breakthroughs of the theories and methods of brain-like intelligence and intelligent equipment with strong interpretability and generalization ability, and finally their applications in major engineering projects.