Abstract: When a group G acts by isometries on a CAT(0) space, this action extends to an action by homeomorphisms of the group on the boundary of the space. I would like to discuss the topology of this boundary as well as the action on this boundary using some interesting examples coming from some fairly elementary groups. I will discuss why this line of study can be quite fruitful when trying to understand the properties of the group and finally, some of the open questions in the area.