Aquatic flow over a submerged vegetation canopy is a ubiquitous example of flow adjacent to a permeable medium. Aquatic canopy flows, however, have two important distinguishing features. Firstly, submerged vegetation typically grows in shallow regions. Consequently, the roughness sublayer, the region where the drag length scale of the canopy is dynamically important, can often encompass the entire flow depth. In such shallow flows, vortices generated by the inflectional velocity profile are the dominant mixing mechanism. Vertical transport across the canopy-water interface occurs over a narrow frequency range centered around fv (the frequency of vortex passage), with the vortices responsible for more than three-quarters of the interfacial flux. Secondly, submerged canopies are typically flexible, coupling the motion of the fluid and canopy. Importantly, flexible canopies can exhibit a coherent waving (the monami) in response to vortex passage. This waving reduces canopy drag, allowing greater in-canopy velocities and turbulent stresses. As a result, the waving of an experimental canopy reduces the canopy residence time by a factor of four. Finally, the length required for the set-up and full development of mixing-layer-type canopy flow is investigated. This distance, which scales upon the drag length scale, can be of the same order as the length of the canopy. In several flows adjacent to permeable media (such as urban canopies and reef systems), patchiness of the medium is common such that the fully developed condition may not be representative of the flow as a whole.