We address the task of inferring the future actions of people from noisy visual input. We denote this task activity forecasting. To achieve accurate activity forecasting, our approach models the effect of the physical environment on the choice of human actions. This is accomplished by the use of state of-the-art semantic scene understanding combined with ideas from optimal control theory. Our unified model also integrates several other key elements of activity analysis, namely, destination forecasting, sequence smoothing and transfer learning. As proof-of-concept, we focus on the domain of trajectory-based activity analysis from visual input. Experimental results demonstrate that our model accurately predicts distributions over future actions of individuals. We show how the same techniques can improve the results of tracking algorithms by leveraging information about likely goals and trajectories.