Differential subordinations in harmonic mappings

Differential subordination of analytic functions proved to be useful in many applications. The book of Miller and Mocanu ((2000) Differential Subordinations. In Theory and applications, monographs and textbooks in pure and applied mathematics, vol 225. Marcel Dekker Inc, New York) sums up most of the advancement in the field and the references to the date of its publication. The theory of harmonic mappings can benefit from this theory. We attempt to discuss some aspects of this generalization.