The study of animal movement has a rich history in ecology, and understanding the drivers of movement is a key ecological challenge. Recent technological advances have transformed the study of movement, but the underlying theory and data analysis methods have not kept pace with this empirical progress. Movement theory is currently based on an outdated, unrealistic, and statistically fragile formalism: that of discrete-step correlated random walk models, where spatiotemporal autocorrelation is ignored and quantifying step-length and turn-angle distributions is the focus. In contrast, we view movement as continuous multivariate stochastic process that is sampled at discrete times. In this formalism, the autocorrelation function (ACF) describing a movement path is the single most informative quantity that can be extracted from movement data. We build on techniques from both physics and geostatistics to develop robust and general methods for estimating ACFs from available movement data. With a parameterized ACF in hand, a huge range of key analyses that help understand movement can be conducted, including: identification of multiple movement behaviors, quantification of relationships between the environment and movement, estimation of home range and space use, identification of periodic or repeating behaviors, interpolation and forecasting, identification of characteristic time and length scales, and path length and energy budget estimation. Along the way, I will talk about my experiences in collaborating with physicists over the years, the strengths and weaknesses of each side, and where I think opportunities for improvement lie.