We present various generalizations of the theory of linearly solvable optimal control. One generalization is the extension to the game theoretic and risk-sensitive setting, which requires replacing KL costs with Renyi divergences. Another extension is the derivation of efficient policy gradient algorithms that only need one to sample the state space (rather than the state-action space) for various problem formulations (finite horizon, infinite horizon, first-exit, discounted). For the finite horizon case, we show that the PI^2 algorithm (Policy Improvement with Path Integrals) can be seen as a special case of our policy gradient algorithms when applied to a risk-seeking objective. Finally, we present applications of these policy gradient algorithms to various problems in movement control and power systems.