In this review, we delve into the fascinating realm of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) in the field of image processing and computer vision. We thoroughly examine the principles, features, and architectures of both CNNs and ViTs, shedding light on their unique characteristics and methodologies. Our analysis encompasses a discussion on the strengths and limitations of CNNs, exploring their ability to capture local features through convolutional layers and hierarchical feature extraction. We highlight their remarkable achievements in image classification, object detection, and semantic segmentation tasks. Additionally, we explore the challenges faced by CNNs, such as their limited capability in capturing global context and their computational requirements for processing high-resolution images. Furthermore, we delve into the emergence of Vision Transformers as a promising alternative to traditional CNNs. We unravel their key components, including self-attention mechanisms, positional encodings, and tokenization strategies. We examine their ability to capture long-range dependencies and contextual information, thereby enabling effective modeling of global relationships in images. Moreover, we discuss their applications in image classification, object detection, and image generation tasks, showcasing their potential to revolutionize computer vision. Throughout the review, we highlight the synergistic relationship between CNNs and ViTs, emphasizing their complementary strengths. We present recent advancements in hybrid architectures that combine both methods, aiming to leverage the local and global features captured by CNNs and ViTs, respectively. By providing a comprehensive understanding of CNNs and ViTs, as well as their respective applications and limitations, this paper equips readers with valuable insights into the advancements and possibilities within the field of computer vision.