We present two solutions to the global exponential attitude tacking control problem using only attitude information on SO(3). The first approach is based on a combined hybrid observerhybrid controller structure. We derive a hybrid angular velocity observer for rigid body systems, designed directly on SO(3) x R-3, guaranteeing global exponential stability of the zero estimation error. Thereafter, we propose an observer-based attitude tracking control scheme guaranteeing global exponential stability. The second approach consists of introducing an auxiliary dynamical system that generates the necessary damping in the absence of the velocity. We prove that the proposed auxiliary-system-based hybrid controller guarantees global exponential stability as well.