Bayesian methods in cosmology and astrophysics have gained significant traction over the past decade, driven by increasing data complexity and computational power. These methods offer advantages over traditional statistics, providing a consistent framework for handling uncertainty and induction. This review introduces Bayesian probability theory, Bayes' Theorem, and its role in parameter inference and model comparison. It discusses numerical techniques like Monte Carlo Markov Chains and the Bayesian evidence for model selection. Recent developments in cosmological parameter extraction and model building are highlighted, emphasizing the need for advanced statistical tools in modern cosmology. The review addresses the importance of Bayesian methods in overcoming challenges such as limited data, computational complexity, and the need for robust inference. It also explores the philosophical underpinnings of Bayesian probability, including the role of priors and the distinction between frequentist and Bayesian approaches. The text emphasizes the necessity of Bayesian methods in cosmology for accurate parameter estimation and model comparison, particularly in the face of complex data and the need for rigorous statistical analysis. The review concludes with a discussion of the practical applications and future directions of Bayesian methods in cosmology.Bayesian methods in cosmology and astrophysics have gained significant traction over the past decade, driven by increasing data complexity and computational power. These methods offer advantages over traditional statistics, providing a consistent framework for handling uncertainty and induction. This review introduces Bayesian probability theory, Bayes' Theorem, and its role in parameter inference and model comparison. It discusses numerical techniques like Monte Carlo Markov Chains and the Bayesian evidence for model selection. Recent developments in cosmological parameter extraction and model building are highlighted, emphasizing the need for advanced statistical tools in modern cosmology. The review addresses the importance of Bayesian methods in overcoming challenges such as limited data, computational complexity, and the need for robust inference. It also explores the philosophical underpinnings of Bayesian probability, including the role of priors and the distinction between frequentist and Bayesian approaches. The text emphasizes the necessity of Bayesian methods in cosmology for accurate parameter estimation and model comparison, particularly in the face of complex data and the need for rigorous statistical analysis. The review concludes with a discussion of the practical applications and future directions of Bayesian methods in cosmology.