This chapter presents data-driven robust closed-loop monitoring approaches with unknown disturbances, utilizing subspace mapping and adaptive observer techniques. In the subspace-aided approach, a subspace for unknown disturbances is constructed. By analyzing the projection relationships among subspaces of different signals within the process data, the stable kernel representation (SKR) of the closed-loop system under disturbance is identified. It involves constructing a residual generator to effectively decouple the residuals from the unknown disturbances, thereby achieving a data-driven robust closed-loop monitoring strategy. In the adaptive observer approach, a closed-loop adaptive estimation framework against unknown disturbances is presented to cope with the correlation between control inputs and noises by integrating the prior knowledge of the controller. An observer-based joint estimation algorithm is constructed using the noise-independent variable as new input, which solves the biased estimation problem under closed-loop feedback and achieves online disturbance estimation and real-time correction with parameter and state estimates.