This chapter has two aims: Unknown input observers (UIOs) and disturbance observer-based control (DOBC) schemes are reviewed. In the unified framework of control and detection, the well-established DOBC schemes are explored. It is showcased that the compensation of the unknown input vector, a key step in the DOBC schemes, is indeed a special case of the output residual generation embedded in the unified framework of control and detection. Furthermore, general existence conditions to achieve a decoupling of closed-loop dynamics from the disturbance are provided. Concerning DOBC design for systems with uncertainties, the stability concern is closely examined. Projection and co-inner-based LS estimation is then applied to unknown inputs. Projection-based LS estimation is also used for uncertainty estimation, requiring backward computations. This inspires the concept of fault-tolerant observers learned through a reinforcement-learning-style (RL) iteration, dual to RL-aided LQ optimal control. The chapter concludes with an observer-based fault-tolerant LQ control scheme as an example of applying LS estimation algorithms to fault-tolerant control and performance recovery.