This paper presents a detailed and comprehensive review of image compression methods, emphasizing their role in optimizing both storage and transmission efficiency across various domains, from everyday use in social media to specialized applications like medical imaging and satellite data processing. We systematically explore both traditional and contemporary image compression techniques, categorizing them into lossless and lossy methods, transform-based approaches, and the latest advancements in machine learning-based compression. Lossless compression techniques, including Run-Length Encoding (RLE), Huffman Coding, Lempel-Ziv-Welch (LZW), and the Portable Network Graphics (PNG) format, are discussed for their ability to preserve image quality perfectly, albeit at the cost of relatively lower compression ratios. Conversely, lossy compression methods, such as JPEG and fractal compression, offer significant file size reduction by discarding non-essential data, while still maintaining acceptable visual quality for many practical applications. We further delve into transform-based approaches like Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT), which form the backbone of popular standards such as JPEG and JPEG 2000, enabling more efficient data representation in the frequency domain. Additionally, the study highlights emerging machine learning and deep learning techniques, such as autoencoders and Generative Adversarial Networks (GANs), that are pushing the boundaries of image compression by achieving unprecedented compression ratios while minimizing perceptual loss in image quality. Through a comparative analysis, we evaluate these methods based on multiple performance metrics, including compression ratio, computational complexity, image fidelity (measured via Peak Signal-to-Noise Ratio, PSNR, and Structural Similarity Index, SSIM), and their practical applications across different industries. Our findings suggest that while traditional methods such as JPEG, PNG, and JPEG 2000 remain widely adopted due to their simplicity and efficiency, emerging techniques driven by deep learning show great potential in adapting to specific image characteristics, achieving higher compression ratios, and better preserving image quality under extreme compression. Finally, this paper identifies key challenges and trends in the field, such as the increasing computational demands of advanced techniques, the need for adaptive compression strategies, and the importance of standardization for broad industry adoption. We conclude that while traditional methods will continue to play a significant role, the future of image compression lies in the integration of machine learning and content-aware technologies that dynamically optimize compression performance across diverse image types and application contexts.