This paper deals with the attitude stabilizing control problem for a rigid spacecraft in the presence of model uncertainties, external disturbances, and actuator faults when delay effects and control input constraints are taken into consideration. First, a backstepping method is introduced in the control design for compensating unknown delays in inputs. Then, a disturbance observer is investigated for estimating model uncertainties, external disturbances, and actuator fault effects. The backstepping controller is augmented with the reconstructed information provided by the disturbance observer to make the closed-loop system insensitive to disturbances and faults. Next, the proposed observer–controller structure is redesigned to deal with control constraints. Rigorous proofs show that the developed control under simple sufficient conditions can render the system globally input-to-state stable (ISS). Numerical simulations are presented to illustrate the effectiveness of the proposed controllers.