Quantum sampling algorithms have claimed quantum computation beyond the limits of classical computation. Photonic boson-sampling was one of the first non-universal, noisy, intermediate-scale models for quantum computing. The milestone experimental demonstration, Jiuzhang, claimed to outperform cutting-edge supercomputers, heralding the onset of the post-classical computational era in 2020. Nevertheless, classical algorithms are developing rapidly to catch up, narrowing the gap between classical and quantum computation. In this article, we provide a comprehensive review of theoretical and experimental developments in boson-sampling, from first principles to cutting-edge experiments achieving quantum computational advantage.