Having once upon a time been a physicist I have come to study dynamical systems, the modern mathematical theory of systems, such as in classical dynamics, that evolve in time. The motivations for this field come from classical and celestial mechanics as well as, more recently, population dynamics, meteorology, economics, physiology, neuroscience, medicine, genomics, i.e. all across the natural and social sciences. In the modern theory of these systems the central aim is often to answer qualitative questions about long-term behavior directly from a study of the governing laws. The grandest of these questions is whether the solar system is stable (or whether instead, the earth might, without external influences, leave the solar system for good at some point). just over 100 years ago this question started the modern theory of dynamical systems and led to the first glimpse of "chaos", and it led to another quantum leap, the KAM-theory of "order", in the 1950s. "Chaos theory" is a popular name for the study of dynamics in which the cumulative effects of the tiniest discrepancies grow exponentially over time and give rise to behavior that looks random and unpredictable. (If two people with different calculators start with x=0.3, compute 4⋅x⋅(1−x) and repeatedly apply the same procedure to the output of the previous step, they will likely quite soon find wild mismatches between their results due to accumulated deviations from differences in rounding.) Hyperbolic dynamics is the mathematical study of these systems, and much of my work has been in uniformly hyperbolic dynamics, which represents this sensitivity to initial conditions in the purest and strongest way and has been called the crown jewel of dynamical systems. For a pure mathematician this is a beautiful subject to study because in these systems the truly messy long-term behavior of any particular time evolution coexists with smooth and orderly global structures in the space of possible states whose study on one hand provides a way of understanding the possible long-term behaviors and on the other hand can provide insights into the origins of the system, for example whether it arises from an algebraic system. It is an exciting field for me because in addition to intrinsic beauty it provides interactions with other fields of mathematics (mostly differential geometry, but also number theory and coding theory, for example). Moreover, the study of hyperbolic dynamics blends into the study of real-world systems with complex behavior, providing methods and concepts to the sciences for describing, classifying, studying and understanding chaotic behavior, such as the intrinsic difficulty of weather prediction, the diagnosis of an impending heart attack from the decreasing (!) complexity of a patient's heart beat or the exquisitely subtle design of a chaotic trajectory for the Genesis spacecraft. I have enjoyed doing and publishing research in this field, writing expository articles at every level, as well as writing and editing books (see the covers), organizing conferences, editing journals and working with colleagues from several continents. My largest single mathematical footprint is Introduction to the Modern Theory of Dynamical Systems, which is among the top 50 most cited mathematics books.