We present some recent results on the topic of quasiconformal harmonic maps. The main result is that every quasiconformal harmonic mapping $w$ of $C^{1,\mu}$ Jordan domain $\Omega_1$ onto $C^{1,\mu}$ Jordan domain $\Omega$ is Lipschitz continuous, which is the property shared with conformal mappings. In addition, if $\Omega$ has $C^{2,\mu}$ boundary, then $w$ is bi-Lipschitz continuous. These results have been considered by the authors in various ways.