Language models (LMs) built upon deep neural networks (DNNs) have recently demonstrated breakthrough effectiveness in software engineering tasks like code generation, code completion, and code repair. This has paved the way for the emergence of LM-based code optimization techniques, which are pivotal for enhancing the performance of existing programs, such as accelerating program execution time. However, a comprehensive survey dedicated to this specific application has been lacking. To address this gap, we present a systematic literature review of over 50 primary studies, identifying emerging trends and addressing 11 specialized questions. The results disclose five critical open challenges, such as balancing model complexity with practical usability, enhancing generalizability, and building trust in AI-powered solutions. Furthermore, we provide eight future research directions to facilitate more efficient, robust, and reliable LM-based code optimization. Thereby, this study seeks to provide actionable insights and foundational references for both researchers and practitioners in this rapidly evolving field.
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