  Rich data generating mechanisms are ubiquitous in this age of information and
require complex statistical models to draw meaningful inference. While Bayesian
analysis has seen enormous development in the last 30 years, benefitting from
the impetus given by the successful application of Markov chain Monte Carlo
(MCMC) sampling, the combination of big data and complex models conspire to
produce significant challenges for the traditional MCMC algorithms. We review
modern algorithmic developments addressing the latter and compare their
performance using numerical experiments.
