Observational data becomes increasingly complex. The ability to learn from new observations is often limited not by the amount of data, but by the sophistication of our analysis tools and the quality of our physical models. Standard statistical techniques, e.g., Markov Chain Monte Carlo, severely limit model realism and complexity, due to their high simulation requirements and limitation on the number of free parameters. However, likelihood-free (or simulation-based) inference algorithms can break through these barriers in surprising ways. I will introduce two of these algorithms and present cosmology and gravitational wave inference examples.