The rapid advancement of foundation models—large-scale neural networks trained on diverse and extensive datasets—has revolutionized the artificial intelligence (AI) field. These models have driven unprecedented progress in areas such as natural language processing, computer vision, and scientific discovery. However, the sheer size of these models, often with parameters numbering in the billions or even trillions, presents significant challenges when adapting them to specific downstream tasks. Low-Rank Adaptation (LoRA) has emerged as a promising solution to this problem. LoRA offers a parameter-efficient mechanism to fine-tune foundation models with minimal additional computational cost. This review provides the first comprehensive overview of LoRA technology, extending beyond large language models to encompass a broader range of foundation models. It delves into the latest foundational techniques, emerging frontiers, and practical applications of LoRA across multiple fields. The review begins by explaining the core principles of LoRA. Instead of fine-tuning all the parameters of a foundation model, LoRA focuses on adjusting a smaller, low-rank matrix that effectively captures the necessary changes to the model's weights. This approach significantly reduces the number of parameters that need to be updated, making the process more efficient and less resource-intensive. In the context of natural language processing (NLP), LoRA has been particularly effective. It allows researchers to fine-tune massive language models, such as BERT and GPT, for specific tasks like sentiment analysis and machine translation without the need for extensive retraining. Similarly, in computer vision, LoRA can be applied to large image recognition models to enhance their performance on niche datasets, improving accuracy and reducing the training time required. The review also highlights recent advancements in the application of LoRA to other AI domains. For example, it has shown promise in scientific research, where it can be used to adapt deep learning models for specific scientific tasks, such as analyzing large-scale astronomical data or predicting molecular properties. These applications underscore the versatility and broad applicability of LoRA. Despite its benefits, LoRA faces several key challenges. The first is theoretical understanding: researchers need to delve deeper into the mathematical principles behind why LoRA works and how it can be optimized further. Another challenge is scalability: while LoRA reduces parameter updates, it must still be adapted to work efficiently on increasingly larger models and datasets. Finally, robustness is a concern: LoRA’s effectiveness can vary depending on the specific task and dataset, and more research is needed to ensure consistent performance across different applications. The review concludes by discussing future research directions. Potential areas of focus include developing more sophisticated low-rank matrices, exploring methods to integrate LoRA with other parameter-efficient techniques, and enhancing the interpretability of LoRA-adapted models. These efforts aim to refine LoRA and make it a more reliable and accessible tool for AI researchers and practitioners. Overall, this comprehensive review of LoRA serves as a valuable resource for those interested in efficient adaptation of foundation models. It not only consolidates current knowledge but also points to promising areas for further investigation, paving the way for more capable and efficient AI systems in the future.