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The goal of this tutorial is to provide attendees with a basic understanding of how information-theoretic tools and techniques can apply to problems of neural inference, both in acquiring data and in using it to obtain relevant inferences. We will use three broad yet concrete motivating problems, carefully chosen to illustrate the breadth of information-theoretic techniques that can be applied to this field. We will present the necessary neuroscientific background and identify key areas of neuroscience research that stand to benefit from the information theory perspective. Attendees should leave the tutorial feeling excited to explore new problems that are, at their core, information theory problems, but can have meaningful impacts in how we understand, sense, and stimulate the brain. The attendees will also obtain concrete pointers to start their work on these problems, including links to a) relevant publicly available data; b) new data obtained by our team; c) software and neural models to enable data analyses; and d) key researchers in the neuroscience and neurotechnology field who may benefit from information theory collaborators. Following an overview of the tutorial material and a summary of relevant neuroscientific background, we will present a collection of open problems at the cutting edge of neuroscience research through three motivating applications: traveling waves, inferring encoding and dynamic processes in neural circuits, and closing the loop.