Target tracking research has been of interest to several different groups of researchers from different perspectives. An event of perhaps greatest importance in the history and development of target tracking research is the new trend in the architectural revolution in current algorithms and techniques that are used for target tracking, i.e., the advent of neural networks and their applications to nonlinear dynamical systems. It is established in the literature that the mathematical complexity of the state-of-the-art tracking algorithms has gone far beyond the computational power of conventional digital processors. Since the introduction of Kalman filtering, several powerful mathematical tools have been added to target tracking techniques, e.g., probabilistic data association, correlation and gating, evidential reasoning, etc. All these methods have one thing in common: they track targets rather differently from the way natural systems do. It is rather difficult to come up with a sound mathematical proof and verification of the concept for different parallel distributed architectures that seem appropriate for a general class of target tracking applications. However, the volume of contributions within the last decade in the application of various neural network architectures to different classes of target tracking scenarios can not simply be ignored. Therefore, the various neural-network-based tracking algorithms that have been introduced since 1986 are classified and addressed and their common views as well as their differences in results and in architectures are discussed. The role of mathematics in each of these algorithms and the extent that conventional methods are used in conjunction with the neural-network-based techniques are also addressed.