  In this paper, we establish an improved coefficient bounds for quasiregular
and elliptic harmonic mappings and
  using these bounds we establish Landau-Bloch type theorem for
$(K,K')$-elliptic and K-quasiregular harmonic
  mappings in plane. Furthermore, we prove the coefficient estimates for
$K$-quasiconformal harmonic self maps defined on the unit disk $\mathbb{D}$.
