This is an announcement for the paper “A characterization of superreflexivity through embeddings of lamplighter groups” by Mikhail I. Ostrovskii<https://arxiv.org/search/math?searchtype=author&query=Ostrovskii%2C+M+I>, Beata Randrianantoanina<https://arxiv.org/search/math?searchtype=author&query=Randrianantoanina%2C+B>. Abstract: We prove that finite lamplighter groups $\{\mathbb{Z}_2\wr\mathbb{Z}_n\}_{n\ge 2}$ with a standard set of generators embed with uniformly bounded distortions into any non-superreflexive Banach space, and therefore form a set of test-spaces for superreflexivity. Our proof is inspired by the well known identification of Cayley graphs of infinite lamplighter groups with the horocyclic product of trees. We cover $\mathbb{Z}_2\wr\mathbb{Z}_n$ by three sets with a structure similar to a horocyclic product of trees, which enables us to construct well-controlled embeddings. https://arxiv.org/abs/1807.06692