To a uniformly locally finite metric space $X$ one can associates a family of C*-algebras known as Roe-type algebras. These were introduced, for index theoretic purposes, with the aim of catching algebraically the large-scale geometry of the metric space of interest. They since have found applications in many areas of mathematics, such as the geometry of manifolds, topological dynamics, and mathematical physics. We are interested in the following question: What can one say about the relation between two spaces $X$ and $Y$ if their Roe-type algebras are isomorphic? For instance, if the algebras are isomorphic, does it follow that the spaces have the same geometry in some sense? Answers to the above question depend of course on which Roe-type algebras one considers. Here, we focus on three of them: the uniform Roe algebra, the uniform Roe corona, and the Higson corona. This is partially based on joint work with Baudier, Braga, Farah, Khukhro and Willett, or with subsets of the above list.