Is it possible to compute effectively the minimal value of a multivariate function without computing its derivative? The general answer is "No", unless the function is convex. For convex functions one can find the minimum with any relative precision involving only values of the functions. Such algorithms of derivative-free minimization are quite efficient (at least, theoretically) even for very large number of variables. They are based on the geometrical idea of the cutting-plane scheme. We discuss the developing of this method in various versions (ellipsoid method, method of simplices, hit-and-run algorithm, etc.) and see why is that difficult to put the derivative-free minimization in hight dimensions to practice, despite their theoretical efficiency.