Cross-shelf exchange dominates the pathways and rates by which nutrients, biota, and materials on the continental shelf are delivered and removed. This follows because cross-shelf gradients of most properties are usually far greater than those in the alongshore direction. The resulting transports are limited by Earth's rotation, which inhibits flow from crossing isobaths. Thus, cross-shelf flows are generally weak compared with alongshore flows, and this leads to interesting observational issues. Cross-shelf flows are enabled by turbulent mixing processes, nonlinear processes (such as momentum advection), and time dependence. Thus, there is a wide range of possible effects that can allow these critical transports, and different natural settings are often governed by different combinations of processes. This review discusses examples of representative transport mechanisms and explores possible observational and theoretical paths to future progress.