The Zappa-Szep product originated from group theory. It can be viewed as a generalization of the semi-direct product, where it encodes a two-way interaction instead of a one-way action. One can also view the Zappa-Szep product as a decomposition of a group as a product of two subgroups. Moving towards operator algebras, we want to understand what a Zappa-Szep product in operator algebras should be. In this talk, I will first present a Zappa-Szep product of a Fell bundle with a groupoid, as a generalization of groupoid actions on Fell bundles. Under this perspective, we proved a generalized imprimitivity theorem arising from such two-way interactions that generalized several classical results of cross-products. I will also present some recent progress on the Zappa-Szep product of C*-algebras arising more intrinsically from Cartan subalgebras. This presents a new way of understanding the Zappa-Szep product using the so-called factorisation map. This realization allows us to define the Zappa-Szep of twisted groupoids, which arises naturally as the Weyl groupoids from Cartan subalgebras. This is a joint work with Anna Duwenig.