I review a class of hybrid models of neurons that combine continuous spike-generation mechanisms and a discontinuous ‘after-spike’ reset of state variables. Unlike Hodgkin–Huxley-type conductance-based models, the hybrid spiking models have a few parameters derived from the bifurcation theory; instead of matching neuronal electrophysiology, they match neuronal dynamics. I present a method of after-spike resetting suitable for hardware implementation of such models, and a hybrid numerical method for simulations of large-scale biological spiking networks.