I will introduce G-algebroids — structures related to the symmetries and low-energy effective descriptions of membranes, strings, and particles. I will describe some basic properties of these algebroids and show how they relate to the more standard Lie and Courant algebroids. I will finish by discussing the main classification results and some (spherical) examples. This is a joint work with M. Bugden, O. Hulik, and D. Waldram.