Summary: The targets of this article are twofold. The first one is to give a survey on bilinear decompositions for products of functions in Hardy spaces and their dual spaces, as well as their variants associated with the Schrödinger operator on Euclidean spaces. The second one is to give a new proof of the bilinear decomposition for products of functions in the Hardy space \(H^1\) and BMO on metric measure spaces of homogeneous type. Some applications to div-curl lemmas and commutators are also presented.