Large scale geometry studies metric spaces observed from afar — for example, it identifies reals with integers. A great source of examples in this theory is provided by warped cones of J. Roe. Given a continuous action of a discrete group on a compact metric space, one can form the infinite cone over the space and then "warp" its metric by introducing "shortcuts" along the group action. We will discuss how properties of the action (both topological and ergodic) are reflected in large-scale properties of the resulting warped cone. This includes joint work with Piotr Nowak.