If $S$ is the graph of a minimal surface, then when given parametrically by the Weierstrass representation, the first two coordinate functions give a univalent harmonic mapping. In this paper, the starting point is a univalent harmonic mapping $f$ of the unit disk $U$. A height function is defined on an appropriate Riemann surface over the range of $f$ which satisfies the minimal surface equation away from the branch points. This height function is then used to obtain function theoretic information about $f$.