Image classification is one of the earliest and most fundamental approaches in computer vision (CV). In the literature, a wide variety of methods have been proposed, ranging from handcrafted feature-based methods to deep-learning-based approaches such as Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs). Each new method has been developed to address the shortcomings of previous methods and achieve higher performance. Image classification is a broad field of study in contemporary scientific research. In this study, image classification methods are comprehensively examined across five distinct application domains: (1) General-purpose vision tasks, (2) Healthcare and medical imaging, (3) Agriculture and environmental monitoring, (4) Remote sensing and Earth observation, (5) Industrial automation and quality inspection. The study first explains classical image classification techniques based on handcrafted features and the corresponding classifiers. It then addresses CNN and ViT models, which are widely used in the literature, analyzing them in terms of architectural innovations, parameter efficiency, and computational complexity. This review covers studies published between 2014 and 2026, with a particular focus on recent developments from 2022 to 2026. Ten datasets were cataloged for each domain; the datasets' characteristics, class distributions, and primary application areas were examined in detail. Additionally, 50 representative real-world applications across these domains were analyzed. The study also addresses the challenges encountered in image classification, and finally discusses future directions.