In this talk, I will review the Elekes-Szabó theorem and its proof, with the emphasis on the use of the group configuration theorem. I will then talk about a recent work joint with Martin Bays on generalisations of the Elekes-Szabó theorem to asymmetric and higher dimensional cases, and mention how to go beyond the group configuration theorem to obtain these results. As an application, we obtain asymmetric and higher dimensional generalisations of the Elekes-Ronyai theorem.