This paper formulates and studies a model of hybrid impulsive and switching Hopfield neural networks (NNs). Using switching Lyapunov functions and a generalized Halanay inequality, some general criteria, which characterize the impulse and switching effects in aggregated form, for asymptotic and exponential stability of such NNs with arbitrary and conditioned impulsive switching are established. Several numerical examples are given for illustration and interpretation of the theoretical results.