The Szemeredi regularity lemma is crucial in graph limit theory.It is a basic tool to study large dense graphs: e.g. how to consider similarity, approximation by small graphs, how local and global properties are related to each other. It provides important new bridge between graph theory and other fields like analysis, probability, topology.Focusing on these aspects, I will give a reiew on some parts of limit theory - which developed in the last few years in the center with Laszlo Lovasz.