  Simulation-based methods for statistical inference have evolved dramatically
over the past 50 years, keeping pace with technological advancements. The field
is undergoing a new revolution as it embraces the representational capacity of
neural networks, optimisation libraries and graphics processing units for
learning complex mappings between data and inferential targets. The resulting
tools are amortised, in the sense that they allow rapid inference through fast
feedforward operations. In this article we review recent progress in the
context of point estimation, approximate Bayesian inference, summary-statistic
construction, and likelihood approximation. We also cover software, and include
a simple illustration to showcase the wide array of tools available for
amortised inference and the benefits they offer over Markov chain Monte Carlo
methods. The article concludes with an overview of relevant topics and an
outlook on future research directions.
