Group actions of a countable group on a measure space give rise to interesting dynamical systems, and studying the associated orbit equivalence relations has been the subject of a lot of study over many years. In this talk we will consider some natural constructions and discuss classification results for such equivalence relations. In particular, we will study how the behavior of certain central sequences implies structural results on the involved equivalence relations and their products. All necessary notions will be introduced during the talk. This is partially based on joint work with Adrian Ioana.