We study Levi harmonic maps, i.e., C ∞ solutions f:M→M′ to $\tau_{\mathcal{H}} (f) \equiv \operatorname{trace}_{g} ( \varPi_{\mathcal{H}}\beta_{f} ) = 0$ , where (M,η,g) is an (almost) contact (semi) Riemannian manifold, M′ is a (semi) Riemannian manifold, β f is the second fundamental form of f, and is the restriction of β f to the Levi distribution ${\mathcal{H}} = \operatorname{Ker}(\eta)$ . Many examples are exhibited, e.g., the Hopf vector field on the unit sphere S 2n+1, immersions of Brieskorn spheres, and the geodesic flow of the tangent sphere bundle over a Riemannian manifold of constant curvature 1 are Levi harmonic maps. A CR map f of contact (semi) Riemannian manifolds (with spacelike Reeb fields) is pseudoharmonic if and only if f is Levi harmonic. We give a variational interpretation of Levi harmonicity. Any Levi harmonic morphism is shown to be a Levi harmonic map.