Medical imaging datasets for research are frequently collected from multiple imaging centers using different scanners, protocols, and settings. These variations affect data consistency and compatibility across different sources. Image harmonization is a critical step to mitigate the effects of factors like inherent differences between various vendors, hardware upgrades, protocol changes, and scanner calibration drift, as well as to ensure consistent data for medical image processing techniques. Given the critical importance and widespread relevance of this issue, a vast array of image harmonization methodologies have emerged, with deep learning-based approaches driving substantial advancements in recent times. The goal of this review paper is to examine the latest deep learning techniques employed for image harmonization by analyzing cutting-edge architectural approaches in the field of medical image harmonization, evaluating both their strengths and limitations. This paper begins by providing a comprehensive fundamental overview of image harmonization strategies, covering three critical aspects: established imaging datasets, commonly used evaluation metrics, and characteristics of different scanners. Subsequently, this paper analyzes recent structural MRI (Magnetic Resonance Imaging) harmonization techniques based on network architecture, network learning algorithm, network supervision strategy, and network output. The underlying architectures include U-Net, Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), flow-based generative models, transformer-based approaches, as well as custom-designed network architectures. This paper investigates the effectiveness of Disentangled Representation Learning (DRL) as a pivotal learning algorithm in harmonization. Lastly, the review highlights the primary limitations in harmonization techniques, specifically the lack of comprehensive quantitative comparisons across different methods. The overall aim of this review is to serve as a guide for researchers and practitioners to select appropriate architectures based on their specific conditions and requirements. It also aims to foster discussions around ongoing challenges in the field and shed light on promising future research directions with the potential for significant advancements.