Based on biological prototype of human brain and improved understanding of the functionality of the neurons and the pattern of their interconnections in the brain, a theoretical model used to explain the information-processing characteristics of the cerebellum was developed independently by Marr (1969) and Albus (1971). Cerebellar model neural network (CMNN) or called as cerebellar model articulation controller (CMAC) was first proposed by Albus in 1974. CMNN is a learning structure that imitates the organization and functionality of the cerebellum of the human brain. That model revealed the structure and functionality of the various cells and fibers in the cerebellum. The core of CMNN is an associative memory which has the ability to approach complex nonlinear functions. CMNN takes advantage of the input-redundancy by using distributed storage and can learn nonlinear functions extremely quickly due to the on-line adjustment of its system parameters. CMNN is classified as a non-fully connected perceptron-like associative memory network with overlapping receptive-fields. It has good generalization capability and fast learning property and is suitable for a lot of applications. This speech will introduce several new CMNN-based adaptive learning systems proposed by me; these systems combine the advantages of CMNN identification, adaptive learning, control technique, signal processing and image classification. In these systems, the on-line parameter training methodologies, using the Lyapunov theorem, are proposed to guarantee the stability and convergence of these systems. Moreover, the applications of these systems in nonlinear systems control, biped robot control, signal processing of communication system, and computer-aided diagnosis of breast nodules are demonstrated.