A powerful combination of a simple logic processor placed in a regular structure is the cellular automaton invented by John von Neumann. The cellular automaton is highly parallel computer architecture. The cellular neural network architecture, invented by L. O. Chua and his graduate student L. Yang, has both the properties: the cell units are nonlinear continuoustime dynamic elements placed in a cellular array. In the circuit implementation, unlike analog computers or general neural networks, the cellular neural/nonlinear network (CNN) cells are not the ubiquitous high-gain operational amplifiers. The CNN is a new paradigm for multidimensional, nonlinear, dynamic processor arrays. The mainly uniform processing elements, called cells or artificial neurons, are placed on a regular geometric grid. The chapter examines several classes of CNN architectures and models depending on the types of grids, processors, interactions, and modes of operation.