In their seminal work about potential theory on calibrated manifolds, Harvey and Lawson introduced ϕ-free submanifolds for a calibration ϕ on a Riemannian manifold. These submanifolds play a similar role like totally real submanifolds of complex manifolds and help us construct Stein-like domains in calibrated manifolds. In this talk, after a brief introduction to potential theory on calibrated manifolds, I will give a survey of results about the geometry and topology of ϕ-free submanifolds in calibrated manifolds with special holonomy.