A hierarchically hyperbolic structure is some kind of coordinate system on a given metric spaces where the coordinates take values in hyperbolic spaces, and it gives a good understanding of the coarse geometry of the space. I will give a brief introduction to this notion and its consequences, discuss a simple criterion to show that a space or group is hierarchically hyperbolic, and some examples of application of the criterion. Speaker(s): Alessandro Sisto (Heriot-Watt University)