Rate-distortion (R-D) methods are essential for image and video compression, balancing the trade-off between data rate and distortion. This paper provides an overview of R-D optimization techniques and their application in practical coding. Classical R-D theory, rooted in Shannon's work, establishes performance bounds for compression systems. However, these bounds are often not tight for complex sources like images or video, necessitating more refined R-D frameworks. R-D theory is applicable not only to source coding but also to data transmission over noisy channels, as it underpins the separation principle in communication systems. Distortion measures must align with human perception, and while MSE is commonly used, perceptually meaningful frameworks can yield better results. R-D optimization techniques, such as Lagrangian optimization and dynamic programming, are crucial for resource allocation in coding systems. For image and video coding, the choice of model is critical. Transform coding, including DCT and DWT, is widely used due to its effectiveness in capturing signal characteristics. The DCT is prevalent in standards like JPEG, while the DWT is gaining traction in JPEG 2000. Adaptive transforms, such as wavelet packet decompositions, offer flexibility in modeling different signal features. In practical coding, operational R-D considerations include system complexity, delay, and buffer management. Standards-based coding requires syntax-constrained R-D optimization, where encoding parameters are chosen to meet specific rate-quality targets. The encoder must select operating points that balance rate and distortion, often involving discrete choices among available modes. The paper highlights the importance of model selection and the impact of perceptual criteria on coding performance. Examples, such as the SPIHT coder outperforming traditional methods, illustrate the effectiveness of advanced R-D techniques. The paper also discusses the challenges of delay-constrained transmission and buffer control in video coding, emphasizing the need for efficient resource allocation. Overall, R-D optimization is vital for achieving efficient and high-quality image and video compression, balancing technical constraints with perceptual quality. The paper underscores the importance of these techniques in modern coding standards and their practical implementation.Rate-distortion (R-D) methods are essential for image and video compression, balancing the trade-off between data rate and distortion. This paper provides an overview of R-D optimization techniques and their application in practical coding. Classical R-D theory, rooted in Shannon's work, establishes performance bounds for compression systems. However, these bounds are often not tight for complex sources like images or video, necessitating more refined R-D frameworks. R-D theory is applicable not only to source coding but also to data transmission over noisy channels, as it underpins the separation principle in communication systems. Distortion measures must align with human perception, and while MSE is commonly used, perceptually meaningful frameworks can yield better results. R-D optimization techniques, such as Lagrangian optimization and dynamic programming, are crucial for resource allocation in coding systems. For image and video coding, the choice of model is critical. Transform coding, including DCT and DWT, is widely used due to its effectiveness in capturing signal characteristics. The DCT is prevalent in standards like JPEG, while the DWT is gaining traction in JPEG 2000. Adaptive transforms, such as wavelet packet decompositions, offer flexibility in modeling different signal features. In practical coding, operational R-D considerations include system complexity, delay, and buffer management. Standards-based coding requires syntax-constrained R-D optimization, where encoding parameters are chosen to meet specific rate-quality targets. The encoder must select operating points that balance rate and distortion, often involving discrete choices among available modes. The paper highlights the importance of model selection and the impact of perceptual criteria on coding performance. Examples, such as the SPIHT coder outperforming traditional methods, illustrate the effectiveness of advanced R-D techniques. The paper also discusses the challenges of delay-constrained transmission and buffer control in video coding, emphasizing the need for efficient resource allocation. Overall, R-D optimization is vital for achieving efficient and high-quality image and video compression, balancing technical constraints with perceptual quality. The paper underscores the importance of these techniques in modern coding standards and their practical implementation.