The emergence of the foundation model era has sparked immense research interest in utilizing pre-trained representations for continual learning~(CL), yielding a series of strong CL methods with outstanding performance on standard evaluation benchmarks. Nonetheless, there are growing concerns regarding potential data contamination within the massive pre-training datasets. Furthermore, the static nature of standard evaluation benchmarks tends to oversimplify the complexities encountered in real-world CL scenarios, putting CL methods at risk of overfitting to these benchmarks while still lacking robustness needed for more demanding real-world applications. To solve these problems, this paper proposes a general framework to evaluate methods for Continual Learning on Dynamic Benchmarks (CLDyB). CLDyB continuously identifies inherently challenging tasks for the specified CL methods and evolving backbones, and dynamically determines the sequential order of tasks at each time step in CL using a tree-search algorithm, guided by an overarching goal to generate highly challenging task sequences for evaluation. To highlight the significance of dynamic evaluation on the CLDyB, we first simultaneously evaluate multiple state-of-the-art CL methods under CLDyB, resulting in a set of commonly challenging task sequences where existing CL methods tend to underperform. We intend to publicly release these task sequences for the CL community to facilitate the training and evaluation of more robust CL algorithms. Additionally, we perform individual evaluations of the CL methods under CLDyB, yielding informative evaluation results that reveal the specific strengths and weaknesses of each method.