Human decision-making often relies on visual information from multiple perspectives or views. In contrast, machine learning-based object recognition utilizes information from a single image of the object. However, the information conveyed by a single image may not be sufficient for accurate decision-making, particularly in complex recognition problems. The utilization of multi-view 3D representations for object recognition has thus far demonstrated the most promising results for achieving state-of-the-art performance. This review paper comprehensively covers recent progress in multi-view 3D object recognition methods for 3D classification and retrieval tasks. Specifically, we focus on deep learning-based and transformer-based techniques, as they are widely utilized and have achieved state-of-the-art performance. We provide detailed information about existing deep learning-based and transformer-based multi-view 3D object recognition models, including the most commonly used 3D datasets, camera configurations and number of views, view selection strategies, pre-trained CNN architectures, fusion strategies, and recognition performance on 3D classification and 3D retrieval tasks. Additionally, we examine various computer vision applications that use multi-view classification. Finally, we highlight key findings and future directions for developing multi-view 3D object recognition methods to provide readers with a comprehensive understanding of the field.