Quantum sampling algorithms provide a rigorous framework for demonstrating computational capabilities beyond the reach of classical systems. Boson sampling, a prominent nonuniversal model for noisy intermediate-scale quantum hardware, has transitioned from theoretical proposals to physical implementation. Since the realization of multiphoton interference in the Jiuzhang experiments at scales intractable for exact classical simulation, Gaussian boson sampling has emerged as a primary photonic architecture for achieving quantum computational advantage. This hardware progress drives parallel advances in classical approximation algorithms, raising the threshold for genuine quantum advantage. In this article, we present a comprehensive review of boson sampling, tracing its development from early complexity-theoretic foundations to recent experimental demonstrations. We further assess efforts toward practical applications and outline the physical pathways for scaling these specialized devices into universal, fault-tolerant photonic quantum computers.