Quality assurance (QA) plays a crucial role in manufacturing to ensure that products meet their specifications. However, manual QA processes are costly and time-consuming, thereby making artificial intelligence (AI) an attractive solution for automation and expert support. In particular, convolutional neural networks (CNNs) have gained a lot of interest in visual inspection. Next to AI methods, the explainable artificial intelligence (XAI) systems, which achieve transparency and interpretability by providing insights into the decision-making process of the AI, are interesting methods for achieveing quality inspections in manufacturing processes. In this study, we conducted a systematic literature review (SLR) to explore AI and XAI approaches for visual QA (VQA) in manufacturing. Our objective was to assess the current state of the art and identify research gaps in this context. Our findings revealed that AI-based systems predominantly focused on visual quality control (VQC) for defect detection. Research addressing VQA practices, like process optimization, predictive maintenance, or root cause analysis, are more rare. Least often cited are papers that utilize XAI methods. In conclusion, this survey emphasizes the importance and potential of AI and XAI in VQA across various industries. By integrating XAI, organizations can enhance model transparency, interpretability, and trust in AI systems. Overall, leveraging AI and XAI improves VQA practices and decision-making in industries.