Arabic Handwriting Recognition (AHR) is a complex task involving the transformation of handwritten Arabic text from image format into machine-readable data, holding immense potential across various applications. Despite its significance, AHR encounters formidable challenges due to the intricate nature of Arabic script and the diverse array of handwriting styles. In recent years, Convolutional Neural Networks (CNNs) have emerged as a pivotal and promising solution to address these challenges, demonstrating remarkable performance and offering distinct advantages. However, the dominance of CNNs in AHR lacks a dedicated comprehensive review in the existing literature. This review article aims to bridge the existing gap by providing a comprehensive analysis of CNN-based methods in AHR. It covers both segmentation and recognition tasks, delving into advancements in network architectures, databases, training strategies, and employed methods. The article offers an in-depth comparison of these methods, considering their respective strengths and limitations. The findings of this review not only contribute to the current understanding of CNN applications in AHR but also pave the way for future research directions and improved practices, thereby enriching and advancing this critical domain. The review also aims to uncover genuine challenges in the domain, providing valuable insights for researchers and practitioners.