© 2017 Meyer, Williamson, Linden and Sahani.Rich, dynamic, and dense sensory stimuli are encoded within the nervous system by the time-varying activity of many individual neurons. A fundamental approach to understanding the nature of the encoded representation is to characterize the function that relates the moment-by-moment firing of a neuron to the recent history of a complex sensory input. This review provides a unifying and critical survey of the techniques that have been brought to bear on this effort thus far—ranging from the classical linear receptive field model to modern approaches incorporating normalization and other nonlinearities. We address separately the structure of the models; the criteria and algorithms used to identify the model parameters; and the role of regularizing terms or “priors.” In each case we consider benefits or drawbacks of various proposals, providing examples for when these methods work and when they may fail. Emphasis is placed on key concepts rather than mathematical details, so as to make the discussion accessible to readers from outside the field. Finally, we review ways in which the agreement between an assumed model and the neuron's response may be quantified. Re-implemented and unified code for many of the methods are made freely available.