We consider the application of optimal control techniques to stochastic models of neural firing. There can be many goals for such control. Here we focus on the targeting of the spiking times of the cell, using a time-varying current applied additively to the current balance equation.We review the theory behind the maximum principle for stochastic optimal control, as well as the challenges posed by its numerical implementation. We then discuss dynamic programming methods for such control, and illustrate its implementation for spike time targeting in the leaky integrate-and-fire model with additive Gaussian white noise. The technique is described in the context where the controller has access to the ongoing voltage. The case where only spike times are available is briefly discussed, along with an outlook into future challenges in designing controls for threshold crossing in drift-diffusion processes.