We show area growth estimates for minimal graphs in the Heisenberg space. We focus on complete graphs and graphs with zero boundary values. For instance, we prove that entire minimal graphs in the Heisenberg space have at most cubic intrinsic area growth. Moreover we explain why height estimates of graphs are useful in the comprehension of the area growth and we show a Collin-Krust type result. Some of our results can be extended to graphs with constant critical mean curvature in homogeneous spaces. Joint work with José Miguel Manzano.