The brain is an information processing machine and thus naturally lends itself to be studied using computational tools based on the principles of information theory. For this reason, computational methods based on or inspired by information theory have been a cornerstone of practical and conceptual progress in neuroscience. In this Review, we address how concepts and computational tools related to information theory are spurring the development of principled theories of information processing in neural circuits and the development of influential mathematical methods for the analyses of neural population recordings. We review how these computational approaches reveal mechanisms of essential functions performed by neural circuits. These functions include efficiently encoding sensory information and facilitating the transmission of information to downstream brain areas to inform and guide behavior. Finally, we discuss how further progress and insights can be achieved, in particular by studying how competing requirements of neural encoding and readout may be optimally traded off to optimize neural information processing.