Calibrations are an important tool in the study of minimal submanifolds. A calibration can be used to show that a particular minimal submanifold is volume minimizing, or, as Harvey and Lawson discovered, a calibration can be used to produce new examples of minimal submanifolds. In the first part of the talk, we will discuss the standard calibration associated to a minimal hypersurface in Euclidean space, and then we will construct a similar calibration associated to a maximal spacelike hypersurface in Minkowski space which can be used to show that a maximal spacelike graph has the largest volume among all spacelike submanifolds with the same boundary. In the second part of the talk, we will introduce Harvey and Lawson’s special Lagrangian calibration and discuss some aspects of the problem of trying to find examples of graphical special Lagrangian cones.