As the physical capabilities of robots increase, so do the potential benefits of autonomous operation. Planning is a central component of an autonomous robotic system. Many practical robotics applications (e.g., setting a table) require reasoning about discrete actions (e.g., placing one plate at each seat) as well as continuous motions (e.g., moving a manipulator). These types of problems form the domain of Task-Motion Planning (TMP). They pose challenges for traditional task planners, as searching continuous, high-dimensional spaces typical of high-DOF manipulators is largely intractable for current discrete search techniques. They are challenging for typical motion planners because the discrete nature of the problems means solutions require sampling on subspaces of measure zero. Additionally, there is a natural hierarchy to the problem that we would like to exploit. As Garret et al. say: “We almost certainly do not want to decide whether to get the frying pan or the steak next by sampling configurations of the robot and the kitchen and testing for paths between them.” This combined task-motion planning problem is not a new research area. The 1971 paper by Fikes and Nilsson introduced a framework for solving such problems that is very similar to what one can find in a modern TMP solver. One notable point, or omission, is an assumption that calculating and representing motion feasibility will be an easy problem. For example they include a problem where a robot must jump onto a box to reach a light switch. They focus on how the robot knows this action is required without mention of how the robot can know if this action is feasible. Forty-seven years later, we still have no general way to determine whether such an action is feasible. Calculating motion feasibility and representing this feasibility to a task planner is still a core problem in TMP research. This thesis presents a new approach to this problem in limited domains, namely tabletop manipulation with a fixed robot arm. For such problems, we show that it is possible to learn a motion feasibility classifier and use it as a heuristic to guide the search for a task-motion plan. The learned heuristic guides the search towards feasible motions and thus reduces the total number of motion planning attempts. A critical property of our approach is the ability to provide robust planning in diverse scenes. We train the classifier on minimal exemplar scenes and then use principled approximations to apply the classifier to complex scenarios in a way that minimizes the effect of errors. By combining learning with planning, our heuristic yields order-of-magnitude run time improvements in diverse tabletop scenarios. Even when classification errors are present, properly biasing our heuristic ensures we will have little computational penalty.