This chapter focuses on artificial neural network models and methods. Although these methods have been studied for over 50 years, they have skyrocketed in popularity in recent years due to accelerated training methods, wider availability of large training sets, and the use of deeper networks that have significantly improved performance for many classification and regression problems. Previous chapters emphasized subspace models. Subspaces are very useful for many applications, but they cannot model all types of signals. For example, images of a single person’s face (in a given pose) under different lighting conditions lie in a subspace. However, a linear combination of face images from two different people will not look like a plausible face. Thus, all possible face images do not lie in a subspace. A manifold model is more plausible for images of faces (and handwritten digits) and other applications, and such models require more complicated algorithms. Entire books are devoted to neural network methods. This chapter introduces the key methods, focusing on the role of matrices and nonlinear operations. It illustrates the benefits of nonlinearity, and describes the classic perceptron model for neurons and the multilayer perceptron. It describes the basics of neural network training and reviews convolutional neural network models; such models are used widely in applications.