In the hierarchy list, the controller tracks are represented by controller icons. The icons can appear differently depending on the controller that is assigned, for instance a Float icon differs from a Float icon. You can also see which specific controllers are assigned to each track by turning on the controllers display in the (on the Track View toolbar, right-click Filters and choose Controller Types from the list). The controller names appear beside the tracks to which they're assigned.
You can assign different controllers to the tracks, affecting the way they respond. The Bezier Controller, assigned by default to all the Position tracks, lets you move objects using the Select and Move transform tool, and converts those movements into Bezier splines. You can adjust the splines in editing mode.