We will discuss how statistical physics techniques developed for the study of stochastic optimization problems can be used to design efficient algorithms for analyzing, controlling and activating extreme trajectories in a variety of cascade processes over graphs and lattices, in which nodes “activate” depending on the state of their neighbors. The problem is in general intractable, with the exception of models that satisfy a sort of diminishing returns property called submodularity (submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems). We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the problem of activating rare trajectories in the dynamics can be solved efficiently on large networks. Examples of preliminary applications range from the maximization of the spread of influence in Threshold Linear Models (Bootstrap percolation) to the minimization of infection processes in SIR models.