Condition monitoring is essential for maintaining industrial machinery by enabling early fault detection and preventing failures. This review focuses on domain-generalized anomalous machine sound detection using deep learning, highlighting acoustic-based methods as non-invasive and informative. We examine key datasets like ToyADMOS and MIMII, which offer diverse sound data representative of real-world scenarios. To address domain shifts common in industrial settings, we explore generalization techniques such as data augmentation, transfer learning, and oversampling to enhance model robustness. The paper reviews reconstruction-based methods using autoencoders and classification-based methods with Convolutional Neural Networks and Transformers for sound anomaly detection. We discuss recent advancements from the DCASE 2024 Task 2 challenge, including the Conditional Autoencoder, Bidirectional Encoder Audio Transformers, and Efficient Audio Transformer, which improve domain shift handling and anomaly detection using only normal samples. Our review underscores the potential of integrating domain generalization with deep learning models for fault detection, contributing to improved predictive maintenance and operational efficiency in industrial systems. Future research should focus on refining these models for more diverse conditions, advancing quality and reliability engineering.