Ocean plastic pollution has escalated into a global environmental crisis, threatening marine ecosystems, biodiversity, and human health. Traditional methods for monitoring and managing this pollution are often labour-intensive, costly, and limited in spatial and temporal scope. This systematic review explores the transformative potential of Artificial Intelligence (AI) and Machine Learning (ML) in revolutionizing the fight against ocean plastic. We survey the current landscape of AI/ML applications across three critical domains: (1) Detection and Monitoring, including the use of satellite, aerial, and drone imagery with computer vision models like Convolutional Neural Networks (CNNs) to identify floating plastic debris and object detection algorithms to classify plastic waste on beaches; (2) Source Prediction and Pathways, leveraging numerical models and ML techniques to forecast plastic accumulation zones and trace pollution back to its sources; and (3) Management and Cleanup, employing robotics, autonomous vehicles, and optimization algorithms for efficient cleanup operations. The review delves into advanced ML methods, including deep learning, reinforcement learning, and graph neural networks, highlighting their specific roles. Furthermore, we integrate a crucial discussion on the financial and economic aspects, analysing how AI can improve cost-efficiency, enable innovative financing models like plastic credit markets, and inform policy. Finally, we address the existing challenges such as data scarcity, model generalization, and computational costs and outline future research directions, advocating for a synergistic human-AI approach to mitigate one of the most pressing planetary challenges of our time.