Purpose of Research: This review paper delves into the transformative impact of computational approaches on drug discovery within molecular biology. It explores how these methods offer efficient and cost-effective solutions to identify and optimize potential drug candidates, addressing the shortcomings of traditional drug discovery methods. Scope of the Experiments: Algorithms, machine learning, artificial intelligence, and quantum mechanics are studied. These approaches analyse large datasets, anticipate drug- target interactions, and improve drug design. Supervised and unsupervised learning techniques enable chemical space exploration, target identification, and compound classification. Bioinformatics and data mining enable target identification, drug discovery, and personalised treatment by analysing large biological databases. Quantum mechanics- based techniques reveal molecular structures, interactions, and reactions, improving drug design and optimisation. Results and Findings: The review demonstrates that computational approaches have the potential to expedite drug discovery by leveraging machine learning, artificial intelligence, quantum mechanics, Big Data, and omics methods. These techniques enable accurate prediction of drug-target interactions and efficient exploration of chemical and biological spaces. The integration of diverse datasets enhances target identification and personalized medicine, while quantum mechanics-based insights improve drug design. Conclusions: Despite their benefits, computational approaches face challenges such as model accuracy, efficiency, and validation. Nonetheless, this review underscores the significance of these approaches and their applications in drug discovery. By addressing challenges and embracing emerging technologies, the field can propel advancements in computational drug discovery. This progress will not only benefit patients but also advance the overall landscape of healthcare.