Motivated by the continuous progress of intelligent manufacturing technologies, the demand for automated welding quality inspection is on the steady rise. This study offers a comprehensive review of the latest advancements and emerging trends in machine vision techniques for weld defect detection, with a specific focus on two primary data modalities: two-dimensional imaging and three-dimensional point cloud data. The reviewed approaches are categorized into two main methodological paradigms: traditional algorithms and deep learning-based methods, and their respective strengths and limitations are systematically examined. In addition, the paper sums up the key challenges in current research and outlines future research directions that aim to enhance model cross-domain adaptability, enable multimodal intelligent collaboration, and establish industrialized closed-loop systems. These endeavors are anticipated to provide theoretical foundations and methodological references for promoting intelligent weld defect detection technologies.