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Large language models (LLMs) are trained on extensive historical corpora, but their ability to understand time and maintain temporal awareness of time-evolving factual knowledge remains limited. Previous studies often neglect the critical aspect of utilizing knowledge from various sources. To address this gap, we introduce EvolveBench, a comprehensive benchmark that evaluates temporal competence along five key dimensions: Cognition, which examines the ability to recall and contextualize historical facts. Awareness, which tests LLMs’ awareness of temporal misalignment between external inputs and the temporal context of a query. Trustworthiness, which assesses whether models can identify and appropriately refuse queries based on invalid timestamps. Understanding, which focuses on interpreting both explicit dates and implicit historical markers. Finally, reasoning evaluates the capacity to analyze temporal relationships and draw accurate inferences. Evaluating 15 widely used LLMs on EvolveBench shows that GPT-4o achieves the highest average EM score of 79.36, while the open-source Llama3.1-70B demonstrates notable strength in handling temporally misaligned contexts with an average score of 72.47. Despite these advances, all models still struggle with handling temporal misaligned context. Our code and dataset are available at https://github.com/zzysjtuiwct/EvolveBench.