We survey some new and old, positive and negative results on a priori estimates, regularity, and rigidity for special Lagrangian equations with or without certain convexity. The "gradient" graphs of solutions are minimal or maximal Lagrangian submanifolds, respectively in Euclidean or pseudo-Euclidean spaces. In the latter pseudo-Euclidean setting, these equations are just Monge-Ampere equations. Development on the parabolic side (Lagrangian mean curvature flows) will also be mentioned.