We discuss necessary and sufficient conditions for the optimality of specific classes of policies in dynamic robust optimization. We then focus on the specific case of affine policies, and show how our conditions can be used to recover and generalize several existing results in the literature. Our treatment draws interesting connections with the theory of discrete convexity (L-natural / M-natural convexity and multimodularity) and global concave envelopes, which may be of independent interest. Time permitting, we also discuss some related applications of the results in the context of a learning and stopping problem.