Likelihood-free inference is an emerging technology that promises tighter constraints on physical parameters than traditional methods in situations where an analytic form of the simulation is intractable. (Anyone who has written down the analytic form of your simulation, I salute you!) We will explore likelihood-free inference from low-level principles and discuss where neural inference ought to outperform traditional inference methods. We will also discuss several (recent) promising results that tackle outstanding practical problems for neural inference in particle physics, before finally surveying the work still to be done to make this a day-to-day reality in the physical sciences.