Over the past years, numerous methods have emerged to automate the quantification of animal behavior at a resolution not previously imaginable. This has opened up a new field of computational ethology, and will in the near future make it possible to quantify in near completeness what an animal is doing as it navigates its environment. The importance of improving the techniques with which we characterize behavior is reflected in the emerging recognition that understanding behavior is an essential (or even pre-requisite) step to pursuing neuroscience questions. The use of these methods, however, is not limited to studying behavior in the wild or in strictly ethological settings. The modern tools for behavioral quantification can be applied to the full gamut of approaches that have historically been used to link brain to behavior, from psychophysics to cognitive tasks, augmenting those measurements with rich descriptions of how animals navigate those tasks. Here we review recent technical advances in quantifying behavior, particularly in methods for tracking animal motion and characterizing the structure of those dynamics. We discuss open challenges that remain for behavioral quantification and highlight promising future directions - with a strong emphasis on emerging approaches in deep learning, the core technology that has enabled the markedly rapid pace of progress of this field. We then discuss how quantitative descriptions of behavior can be leveraged to connect brain activity with animal movements, with the ultimate goal of resolving the relationship between neural circuits, cognitive processes, and behavior.