Service robots are built and developed for various applications to support humans as companion, caretaker, or domestic support. As the number of elderly people grows, service robots will be in increasing demand. Particularly, one of the main tasks performed by elderly people, and others, is the complex task of cleaning. Therefore, cleaning tasks, such as sweeping floors, washing dishes, and wiping windows, have been developed for the domestic environment using service robots or robot manipulators with several control approaches. This article is primarily focused on control methodology used for cleaning tasks. Specifically, this work mainly discusses classical control and learning-based controlled methods. The classical control approaches, which consist of position control, force control, and impedance control , are commonly used for cleaning purposes in a highly controlled environment. However, classical control methods cannot be generalized for cluttered environment so that learning-based control methods could be an alternative solution. Learning-based control methods for cleaning tasks can encompass three approaches: learning from demonstration (LfD), supervised learning (SL), and reinforcement learning (RL). These control approaches have their own capabilities to generalize the cleaning tasks in the new environment. For example, LfD, which many research groups have used for cleaning tasks, can generate complex cleaning trajectories based on human demonstration. Also, SL can support the prediction of dirt areas and cleaning motion using large number of data set. Finally, RL can learn cleaning actions and interact with the new environment by the robot itself. In this context, this article aims to provide a general overview of robotic cleaning tasks based on different types of control methods using manipulator. It also suggest a description of the future directions of cleaning tasks based on the evaluation of the control approaches.