This review explores the role of relative entropy in quantum information theory, emphasizing its importance in quantifying distinguishability between quantum states. The concept of distinguishability is central to information processing, as it determines how much information can be encoded and manipulated in a system. Relative entropy, a measure of the difference between two probability distributions, is shown to be a fundamental quantity in this context. It is proven that relative entropy does not increase with time, implying that states become less distinguishable as they evolve. This property is crucial for understanding the limits of information processing in quantum systems. The review discusses how relative entropy can be used to analyze the efficiency of quantum computation, showing that computation can be viewed as a special form of communication. It also highlights the role of measurement in quantum mechanics and information theory, noting that the efficiency of a measurement can be quantified using relative entropy. The review further connects information theory with thermodynamics and quantum mechanics, showing how information processing relates to entropy and irreversibility. The paper introduces the concept of relative entropy in both classical and quantum contexts, starting with the classical Shannon entropy and then extending it to quantum systems. It discusses the statistical significance of relative entropy, using examples such as the distinguishability of probability distributions and the application of Sanov's theorem. The review also covers the mutual information between two random variables, showing how it can be quantified using relative entropy. The paper then explores the application of relative entropy to classical evolution, demonstrating that it decreases under stochastic processes. This property is important for understanding the dynamics of classical systems and the behavior of probability distributions over time. The review also introduces the Schmidt decomposition, a mathematical tool used to analyze entanglement in quantum systems. It shows how the Schmidt decomposition can be used to express a composite quantum state in terms of orthonormal basis states, highlighting the correlations between subsystems. Overall, the review emphasizes the importance of relative entropy in quantum information theory, showing how it provides a framework for understanding the limits of information processing, the efficiency of quantum computation, and the nature of entanglement in quantum systems.This review explores the role of relative entropy in quantum information theory, emphasizing its importance in quantifying distinguishability between quantum states. The concept of distinguishability is central to information processing, as it determines how much information can be encoded and manipulated in a system. Relative entropy, a measure of the difference between two probability distributions, is shown to be a fundamental quantity in this context. It is proven that relative entropy does not increase with time, implying that states become less distinguishable as they evolve. This property is crucial for understanding the limits of information processing in quantum systems. The review discusses how relative entropy can be used to analyze the efficiency of quantum computation, showing that computation can be viewed as a special form of communication. It also highlights the role of measurement in quantum mechanics and information theory, noting that the efficiency of a measurement can be quantified using relative entropy. The review further connects information theory with thermodynamics and quantum mechanics, showing how information processing relates to entropy and irreversibility. The paper introduces the concept of relative entropy in both classical and quantum contexts, starting with the classical Shannon entropy and then extending it to quantum systems. It discusses the statistical significance of relative entropy, using examples such as the distinguishability of probability distributions and the application of Sanov's theorem. The review also covers the mutual information between two random variables, showing how it can be quantified using relative entropy. The paper then explores the application of relative entropy to classical evolution, demonstrating that it decreases under stochastic processes. This property is important for understanding the dynamics of classical systems and the behavior of probability distributions over time. The review also introduces the Schmidt decomposition, a mathematical tool used to analyze entanglement in quantum systems. It shows how the Schmidt decomposition can be used to express a composite quantum state in terms of orthonormal basis states, highlighting the correlations between subsystems. Overall, the review emphasizes the importance of relative entropy in quantum information theory, showing how it provides a framework for understanding the limits of information processing, the efficiency of quantum computation, and the nature of entanglement in quantum systems.