Hillclimbing is an integral part of every optimization algorithm. One would expect that our standard hillclimbing algorithms can solve nice, unimodal functions e ciently. For example, strictly monotone functions: consider the search space S = f0; 1gn of n-bit strings; then a strictly monotone function f : S ! R is a function that satis es f (x) < f (y) for all di erent strings x, y in S such that xi yi holds for all 1 i n. Strictly montone functions are the easiest imaginable testbed for hillclimbers: The function f always prefers one-bits over zero-bits, so there are always short and clearly labelled paths from any start point to the unique global optimum 11::1. Surprisingly, it has become clear in the last years that many of our standard hillclimbers fail miserably on some strictly monotone functions. In many instances, they need exponential time to nd the optimum. This devastating result has deepened our understanding of hillclimbing techniques, and has given new insights into the mechanisms that are behind some hillclimbing techniques, like selective pressure, step size policies, and population e ects. These insights have also improved our understanding of optimization beyond hillclimbing, in particular of optimization in dynamic environments.