Neuronal phase response curves (PRCs) summarize the relationship between the timing of inputs within a neuron’s spike cycle and the consequent shifts in output spike timing. The form of a neuron’s PRC reflects its mechanism of spike initiation or excitability as well as other influences of membrane conductances on synaptic integration. PRCs are efficient encapsulations of the input-output processing of individual neurons to single perturbations and are powerful devices for the prediction and interpretation of patterned neuronal network activity including synchronization phenomena in connected networks or populations receiving shared input. Thus, application of phase response analysis to neural systems targets the interface of neural computation at the cellular and network levels, one of the most critical and expansive gaps in our understanding of the brain. This volume surveys the diversity of applications of phase response analysis by many of the prominent theoreticians and experimentalists in the Computational Neurosciences. Readers will find a thorough introduction to the foundational concepts underlying phase response analysis, advanced techniques for accurate estimation of neuronal PRCs, and impactful illustrations of both the cellular underpinnings of the phase response properties of neurons and the power of phase response analysis to explain network behavior. Throughout the book, the authors use phase response analysis to elucidate a number of neural systems that are current foci of exciting research in the Computational Neurosciences and are at the forefront of our advancing grasp of the complex mechanisms of brain function and dysfunction.