The past decade has witnessed a step-change in the scale, complexity, and scope of quantum information processing with photonics. Breakthroughs include photonic chips with dense co-integration of a large number of components, deterministic single photon sources with large purity, and high efficiency single photon detectors. Within this framework Boson Sampling is a computational problem that has been proposed as a candidate to obtain an unequivocal quantum computational advantage. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We will review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We will discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered.