Large Language Models (LLMs) have exhibited exceptional performance in software engineering yet face challenges in adapting to continually evolving code knowledge, particularly the frequent updates of third-party library APIs. This limitation, rooted in the static pre-training datasets, often results in non-executable code or implementations with suboptimal safety and efficiency. To this end, we introduce CodeSync, a data engine to identify outdated code patterns and collect real-time code knowledge updates from Python third-party libraries. Building upon CodeSync, we develop CodeSyncBench, a comprehensive benchmark for assessing LLMs' ability to stay synchronized with code evolution, which covers real-world updates for 220 APIs from six Python libraries. Our benchmark offers 3,300 test cases spanning three evaluation tasks and an update-aware instruction tuning dataset of 2,200 training samples. Extensive experiments on 14 LLMs reveal that they struggle with dynamic code evolution, even with the support of advanced knowledge updating methods (e.g., DPO, ORPO, and SimPO). Our CodeSync lays a strong foundation for developing more effective and robust methods for real-time code knowledge updating in the future. The experimental code is available at: https://github.com/CGCL-codes/naturalcc/tree/main/examples/codesync.