  Learning-enabled control systems have demonstrated impressive empirical
performance on challenging control problems in robotics, but this performance
comes at the cost of reduced transparency and lack of guarantees on the safety
or stability of the learned controllers. In recent years, new techniques have
emerged to provide these guarantees by learning certificates alongside control
policies -- these certificates provide concise, data-driven proofs that
guarantee the safety and stability of the learned control system. These methods
not only allow the user to verify the safety of a learned controller but also
provide supervision during training, allowing safety and stability requirements
to influence the training process itself. In this paper, we provide a
comprehensive survey of this rapidly developing field of certificate learning.
We hope that this paper will serve as an accessible introduction to the theory
and practice of certificate learning, both to those who wish to apply these
tools to practical robotics problems and to those who wish to dive more deeply
into the theory of learning for control.
