We review how leaky competing accumulators (LCAs) can be used to model decision making in two-alternative, forced-choice tasks, and we show how they reduce to drift diffusion (DD) processes in special cases. As continuum limits of the sequential probability ratio test, DD processes are optimal in producing decisions of specified accuracy in the shortest possible time. Furthermore, the DD model can be used to derive a speed-accuracy trade-off that optimizes reward rate for a restricted class of two alternative forced-choice decision tasks. We review findings that compare human performance with this benchmark, and we reveal both approximations to and deviations from optimality. We then discuss three potential sources of deviations from optimality at the psychological level--avoidance of errors, poor time estimation, and minimization of the cost of control--and review recent theoretical and empirical findings that address these possibilities. We also discuss the role of cognitive control in changing environments and in modulating exploitation and exploration. Finally, we consider physiological factors in which nonlinear dynamics may also contribute to deviations from optimality.