  While end-to-end learning with fully differentiable models has enabled
tremendous success in natural language process (NLP) and machine learning,
there have been significant recent interests in learning with latent discrete
structures to incorporate better inductive biases for improved end-task
performance and better interpretability. This paradigm, however, is not
straightforwardly amenable to the mainstream gradient-based optimization
methods. This work surveys three main families of methods to learn such models:
surrogate gradients, continuous relaxation, and marginal likelihood
maximization via sampling. We conclude with a review of applications of these
methods and an inspection of the learned latent structure that they induce.
