Szemeredi’s regularity lemma is a powerful tool in extramal graph theory, which had have many applications. In this talk we present several variants of Szemeredi’s original lemma (due to several researchers including Frieze and Kannan, Alon et al., and Lovasz and Szegedy) and discuss their relation to each other. If time permits we may consider several different looking regularity lemmas for hypergraphs of which some, but not all, turn out to be equivalent.