<p>Randomness constitutes a foundational aspect in quantum theory and serves as a key resource for modern science and technology, underpinning breakthroughs in areas such as cryptography, secure communications, and large-scale computational simulations. Randomness from Classical sources are inherently deterministic at the microscopic level, relying on computational pseudo randomness. In contrast, quantum theory provides an intrinsically probabilistic framework where genuine randomness arises fundamentally, independent of any ignorance or incomplete knowledge about the system. This review aims to provide a comprehensive account of the development in <i>device-independent</i> (DI) and <i>semi-device-independent</i> (SDI) randomness certification schemes, with particular focus on dimension witness approaches, quantum steering, and protocols for sequential randomness certification, its expansion and amplification. This work also explores the field from early theoretical proposals to recent experimental milestones, examining generation techniques, their physical origins, and key challenges such as detection efficiency, non-linear witnesses, and temporal correlations in certifying intrinsic randomness. Furthermore, a comprehensive study of the experimental realization of randomness certification across diverse scenarios, along with its applications in modern technologies and its implications for digital security and broader societal advancement, is presented. The discussion concludes by outlining future directions, emphasizing both the foundational significance and the challenges of achieving scalable, practical implementations with direct relevance to public interest.</p>