This paper reviews recent image compression techniques, focusing on classical and region-of-interest (ROI)-based approaches. Image compression is crucial in fields with limited computational resources, such as automotive and telemedicine, where efficient storage, transmission, and decompression are vital. Recent methods prioritize preserving the quality of the ROI while compressing other areas with significant quality loss. The paper analyzes relevant papers from the last decade, highlighting the importance of ROI selection and compression techniques for maintaining diagnostic details in medical images. It also compares classical and hybrid methods, discussing metrics like mean-square error (MSE), peak signal-to-noise ratio (PSNR), compression ratio (CR), and structural similarity index (SSIM). The study emphasizes the balance between file size reduction and image quality, particularly in applications where high fidelity is essential, such as medical imaging. Lossy and lossless compression methods are discussed, with lossy techniques offering higher compression ratios but potentially lower image quality, while lossless methods preserve quality but result in smaller size reductions. ROI-based compression is particularly useful in medical imaging, where critical diagnostic information must be preserved. The paper also explores various compression algorithms, including wavelet transforms, fractal compression, and transform encryption, and evaluates their performance using metrics like PSNR, CR, and MSE. The study concludes that hybrid methods, which apply different compression techniques to different regions of an image, offer a balance between efficiency and quality, making them suitable for applications where both storage and transmission efficiency are critical.This paper reviews recent image compression techniques, focusing on classical and region-of-interest (ROI)-based approaches. Image compression is crucial in fields with limited computational resources, such as automotive and telemedicine, where efficient storage, transmission, and decompression are vital. Recent methods prioritize preserving the quality of the ROI while compressing other areas with significant quality loss. The paper analyzes relevant papers from the last decade, highlighting the importance of ROI selection and compression techniques for maintaining diagnostic details in medical images. It also compares classical and hybrid methods, discussing metrics like mean-square error (MSE), peak signal-to-noise ratio (PSNR), compression ratio (CR), and structural similarity index (SSIM). The study emphasizes the balance between file size reduction and image quality, particularly in applications where high fidelity is essential, such as medical imaging. Lossy and lossless compression methods are discussed, with lossy techniques offering higher compression ratios but potentially lower image quality, while lossless methods preserve quality but result in smaller size reductions. ROI-based compression is particularly useful in medical imaging, where critical diagnostic information must be preserved. The paper also explores various compression algorithms, including wavelet transforms, fractal compression, and transform encryption, and evaluates their performance using metrics like PSNR, CR, and MSE. The study concludes that hybrid methods, which apply different compression techniques to different regions of an image, offer a balance between efficiency and quality, making them suitable for applications where both storage and transmission efficiency are critical.