A surface moving by mean curvature flow with a rapidly oscillating forcing models e.g. the behaviour of a phase boundary in an impure medium. Mathematically, the combination of rapidly varying random or periodic coefficients and geometric evolution is challenging, with open problems even in the periodic case. Phenomena like pinning and power laws for effective velocities can occur, with many more interesting features in the random case. I will sketch the state of the art and difficulties both in the random and periodic case and introduce a simplified model, the so-called random obstacle model.