Enveloping semigroups, introduced by Robert Ellis, are a useful tool in topological dynamics which allows to describe the behavior of systems (equicontinuity, distality, …) in terms of properties of a topological-algebraic structure. Based on this idea, we discuss “enveloping semigroupoids” in this talk and how they can be used to study structured extensions in topological dynamics and ergodic theory. This is based on joint work with Nikolai Edeko, Patrick Hermle and Asgar Jamneshan.