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In Section 1, we recall some basic facts about planar harmonic mappings. In Section 2, we present harmonic analog of the classical Schwarz’lemma and its applications. In Section 3, we include the definition of quasiconfomal mappings along with some basic results and conformal modulus. In Section 4, our main aim is to discuss a lower bound for the module of the image annulus of a univalent harmonic mapping of an annulus. The result obtained by Lyzzaik, Weitsman and Kalaj each by a different method of proof is the first substantial solution for a 39-year open problem that was originally raised in l962 by JCC Nitsche. The problem is actually originated from the study of minimal surfaces.