The compression of images for efficient storage and transmission is crucial in handling large data volumes. Lossy image compression reduces storage needs but introduces perceptible distortions affected by content, compression levels, and display environments. Each compression method generates specific visual anomalies like blocking, blurring, or color shifts. Standardizing efficient lossy compression necessitates evaluating perceptual quality. Objective measurements offer speed and cost efficiency, while subjective assessments, despite their cost and time implications, remain the gold standard. This paper delves into essential research queries to achieve visually lossless images. The paper describes the influence of compression on image quality, appropriate objective image quality metrics (IQMs), and the effectiveness of subjective assessment methods. It also provides an overview of the existing literature, surveys, and subjective and objective image quality assessment (IQA) methods. Our aim is to offer insights, identify challenges in existing methodologies, and assist researchers in selecting the most effective assessment approach for their needs.