This paper presents current approaches for robotic garment folding-oriented 3D deformable object perception and manipulation. A major portion of these approaches are based on 3D perception algorithms that match garments to a model, and are thus model-based. They require a full view of an extended garment, in order to then apply a preprogrammed folding sequence. Other approaches are based on 3D manipulation algorithms that are focused on modifying the pose of the garment, also oriented at matching it with a model. We present our own garment-agnostic algorithm, which requires no model to unfold clothes, and works using a single view from an RGB-D sensor. The unfolding algorithm also has been validated through experiments using a garment dataset of RGB-D sensor data, and additional validation with a humanoid robot platform. Finally, conclusions regarding the current state of the art and on the future trends of these research lines are discussed.