In computational neuroscience, one of the major challenges is to characterize the relationship between a sensory stimulus and the neural response. In this talk I am going to present approximate Bayesian methods to analyze this relationship from two different perspectives. One is the "encoding" perspective which aims for predicting the neural response as accurately as possible when knowing only the sensory input. The second is the "decoding" perspective where one is trying to solve the inverse problem - knowing only the spike-times of a neural population, how can we estimate the sensory signal, which could have led to the observed response? The focus will be on the methods we have developed for a fully Bayesian treatment of these problems with an emphasis on the encoding perspective. As a result, we obtain not only a specific estimate of the quantity of interest (model parameters for the encoding part and stimulus estimate for the decoding part) but also an estimate of the uncertainty. Having access to the uncertainty allows then for further analysis such as feature- and model-selection as well as experimental design.