In this chapter, we introduce the notion of the gradients of Hopfield energy functions and discuss how to employ them for efficient informed asynchronous updates of a Hopfield net. Armed with the corresponding algorithm, we will then demonstrate the use of Hopfield nets as problem solvers. In particular, we will consider a constraint satisfaction problem and a combinatorial optimization problem, show how to set up respective Hopfield net parameters, and then practically evaluate the the problem solving capabilities of Hopfield nets under different initializations and parameterizations. In preparation for things still to come, we finally discuss the characteristics of local search procedures and how more global procedures may overcome some of their limitations.