The Antarctic Slope Current (ASC) is a coherent circulation feature that rings the Antarctic continental shelf and regulates the flow of water toward the Antarctic coastline. The structure and variability of the ASC influences key processes near the Antarctic coastline that have global implications, such as the melting of Antarctic ice shelves and water mass formation that determines the strength of the global overturning circulation. Recent theoretical, modeling, and observational advances have revealed new dynamical properties of the ASC, making it timely to review. Earlier reviews of the ASC focused largely on local classifications of water properties of the ASC's primary front. Here we instead provide a classification of the current's frontal structure based on the dynamical mechanisms that govern both the along‐slope and cross‐slope circulation; these two modes of circulation are strongly coupled, similar to the Antarctic Circumpolar Current. Highly variable motions, such as dense overflows, tides, and eddies are shown to be critical components of cross‐slope and cross‐shelf exchange, but understanding of how the distribution and intensity of these processes will evolve in a changing climate remains poor due to observational and modeling limitations. Results linking the ASC to larger modes of climate variability, such as El Niño, show that the ASC is an integral part of global climate. An improved dynamical understanding of the ASC is still needed to accurately model and predict future Antarctic sea ice extent, the stability of the Antarctic ice sheets, and the Southern Ocean's contribution to the global carbon cycle.