  This paper provides a review of Approximate Bayesian Computation (ABC)
methods for carrying out Bayesian posterior inference, through the lens of
density estimation. We describe several recent algorithms and make connection
with traditional approaches. We show advantages and limitations of models based
on parametric approaches and we then draw attention to developments in machine
learning, which we believe have the potential to make ABC scalable to higher
dimensions and may be the future direction for research in this area.
