We present a historical perspective on ocean mesoscale variability and turbulence, from the physical basis and the first numerical models to recent simulations and forecasts. In the mesoscale range (typically, spatial scales of 100 km and time scales of a month), nonlinearity, and energy cascades were well understood in the 1970s, but the emergence of coherent vortices took place much later. New challenges have arisen with the exploration of the submesoscale regime, where frontal dynamics play a key role and the range of flow instabilities is wider than in the quasi-geostrophic regime. Special focus is placed on the interaction of mesoscale turbulence with the continental slopes. The contrast between the variability on the western and eastern boundaries of an ocean basin is illustrated by numerical simulations of the North Atlantic. On the eastern continental slope, direct forcing of currents by wind fluctuations is more important than it is on the western side of the basin, where forcing by intrinsic mesoscale variability is dominant. Dynamical characteristics of the ocean mesoscale such as these must be taken into account in building forecasting systems. These systems require improved numerical models to represent mesoscale variability with more fidelity. We present our view of the most pressing needs for model development as they relate to the challenges of data assimilation at the mesoscale.