Handling disturbance and model uncertainty is a long-standing but troublesome problem in control design. Accordingly, the disturbance observer (DOB) has received keen interest over decades because it is an easy-to-use tool for robustifying control systems. The core of the DOB-based controller (DOBC) is to estimate and compensate for the combined effect of disturbance and plant uncertainty, and diverse design philosophies have been suggested. In this survey-style paper, we first introduce several representative DOBCs that have been widely employed in the literature, including unknown input observer-based control, extended state observer-based control, inversion DOBC, and nonlinear DOBC, and focus on the rationale behind the estimation of uncertain factors. The state-of-the-art in both the theory and application of these DOBCs are then discussed. Specifically, it is shown that the DOBC theory can contribute to not only classical robust control problems but also emerging research topics, such as multi-agent systems, safety-critical control, and cyber-security. Finally, some challenging issues related to the DOBC are listed, which call for further investigation in the future.