In this chapter, we finally look at Hopfield nets which are rather simple recurrent neural networks. First, we ever so briefly contrast them to other kinds of neural networks and then list and discuss their defining (structural) properties. We then introduce the important notion of the energy function of a neural network and discuss synchronous and asynchronous update mechanisms for running Hopfield nets. For the latter, we then carefully prove the important facts that, if the neurons of a Hopfield net update their individual states one at a time, then the overall state of the network will converge to a stable state of low energy and that this convergence will happen within a finite number of steps. In all of this, we will concentrate on classical Hopfield nets and ignore their modern variants.