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The quality of welded joints is critical to the safety, reliability, and durability of engineering structures in manufacturing, energy, transportation, and shipbuilding. Advances in non-destructive testing (NDT) have enabled the collection of large digital datasets, creating new opportunities for artificial intelligence (AI) in automated weld quality assessment. This paper reviews recent research on AI-based quality control of welded joints, focusing on machine learning, deep learning, computer vision, and real-time monitoring. A systematic review and critical analysis of recent scientific literature examines weld imperfections, major NDT methods, digital datasets, and AI performance in defect detection, classification, segmentation, and quality prediction. The findings show that deep learning architectures, including convolutional neural networks, object detection and segmentation models, hybrid frameworks, and transfer learning, can significantly improve the speed, consistency, and objectivity of weld inspection while achieving high detection performance across different NDT modalities. However, several challenges limit industrial implementation, including insufficient data quality and availability, class imbalance, domain shift, limited model generalization, the lack of standardized benchmark datasets, and the need for explainable and trustworthy AI that complies with industrial standards and regulatory requirements. Unlike previous reviews focused primarily on individual inspection methods or specific AI techniques, this paper integrates advances in NDT, AI, explainable artificial intelligence, and intelligent manufacturing into a unified perspective, highlighting their interrelationships and practical implications for industrial deployment. The findings indicate that AI should support, rather than replace, welding and NDT experts. Future research should focus on multimodal sensing, explainable AI, digital twins, standardized datasets, and real-time intelligent quality control systems for Industry 4.0 and smart manufacturing.