Flows in Nature and in engineering are often complex, forced by external agents, boundary stresses, and internal instabilities, and pervaded by multiscale structures such as eddies, plumes, jets, waves, and turbulence –spanning many orders of magnitude in size. The nonlinear nature of the dynamics implies a coupling between these multiple scales, which often plays a major role in determining mean-flow evolution and is a primary factor limiting our predictive modeling capabilities. In this talk, I will explain cascades, dissipative anomalies, and scale-locality of interactions in the context of the Richardson-Kolmogorov-Onsager theory of incompressible turbulence. I will then discuss related results for compressible flows and for magnetized plasmas. Time permitting, I will preview ongoing efforts in our group to understand multi-scale dynamics in statistically inhomogeneous flows, including those in the ocean and in inertial confinement fusion experiments.