The quest of AI and Robotics researchers to realize fully AI-driven integrated robotic systems has not yet led to such realizations, in spite of great attainments in both research areas.  One of the major hindrances to these realizations is the lack of attention to what we call ``the hybrid reasoning problem''.  This is the problem of jointly reasoning about heterogeneous and inter-dependent aspects of the world, expressed in different forms and at different levels of abstraction. In this talk, I present an approach to hybrid reasoning (or integrated reasoning) for robot applications. This approach constitutes a systematic way of achieving a domain-specific integration of reasoning capabilities.  Its underpinning is to jointly reason about the sub-problems of an overall hybrid problem in the combined search space of mutual decisions. The proposed approach has been applied in several different domains, namely, a waiter robot, an automated industrial fleet management application, and a drill pattern planning problem in open-pit mining.