We talk about a priori Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher  dimensions. The "gradient" graphs of solutions are minimal Lagrangian submanifolds. Our unified approach leads to sharper estimates even for the  previously known three dimensional or convex solution cases. Recentcounterexamples for subcritical phase equations will also be mentioned. This is joint work with Dake Wang.