I will define bounded cohomology of discrete groups illustrated by some examples coming from computing the volumes of locally geodesic simplices in hyperbolic manifolds. We will see that the volume class associated to a tame 3-dimensional hyperbolic structure of infinite volume classifies its geometry up to bi-Lipschitz equivalence. We will also study the behavior of linear combinations of volume classes, and give a geometric interpretation of addition in some special cases. We will also explain what is known for volume classes of representations in higher dimensions and a higher rank setting, if time permits.