This review paper provides a summary of methods in which artificial intelligence (AI) techniques have been applied in the management of variable renewable energy (VRE) systems, and an outlook to future directions of research in the field. The VRE types included are namely solar, wind and marine varieties. AI techniques, and particularly machine learning (ML), have gained traction as a result of data explosion, and offer a method for integration of multimodal data for more accurate forecasting in energy applications. The VRE management aspects in which AI techniques have been applied include optimized power generation forecasting and integration of VRE into power grids, including the aspects of demand forecasting, energy storage, system optimization, performance monitoring, and cost management. Future directions of research in the applications of AI for VRE management are proposed and discussed, including the issue of data availability, types and quality, in addition to explainable artificial intelligence (XAI), quantum artificial intelligence (QAI), coupling AI with the emerging digital twins technology, and natural language processing.