Task and motion planning (TAMP) solvers in robotics combine logical reasoning and geometric motion planning to enable complex, long-horizon behaviors. Despite significant progress in TAMP solvers over the last decade, several core problems remain unsolved, particularly regarding the role that machine learning should play to improve these solvers. In this talk, we will show how to design TAMP solvers that learn to plan better and faster by leveraging past experience of solving similar problems in similar environments. We will present applications of our informed TAMP solver in long-horizon manipulation tasks in chemistry and biology labs, where robot arms can execute a diverse range of long-horizon experiments. In addition to informed task planners, we will discuss how to learn monotone NN heuristics for motion planners in TAMP by imposing quasimetric structure in the network representing the heuristic. Finally, we will discuss open-world perception and mapping methods that have the potential to enable flexible and structured representations for TAMP solvers. We will conclude with a future outlook on the potential role of TAMP solvers in the era of large models for robotics.