Abstract: Quantum computers exploit the incredible possibilities of quantum mechanics to significantly enhance computing power, compared with the computers currently available based on a conventional approach. In this context, it is essential to experimentally demonstrate the potential of quantum computers. Recently, the study of computational problems that produce samples from probability distributions has highlighted a path forward to demonstrate quantum advantage, corresponding to a scenario where a quantum device solves a specific computational problem faster than any classical system, as well as first applications. In particular we will discuss a computational problem that has been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware. 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.