In this paper, we report the consequences induced by the presence of asymmetries in the coupling scheme on the synchronization process of a pair of one-dimensional complex fields obeying Complex Ginzburg Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of modifying synchronization thresholds and play a crucial role in selecting the statistical and dynamical properties of the highly coupled synchronized motion. Possible consequences of such asymmetry induced effects in biological and natural systems are discussed.