Continual learning (CL) aims to learn a non-stationary data distribution and not forget previous knowledge. The effectiveness of existing approaches that rely on memory replay can decrease over time as the model tends to overfit the stored examples. As a result, the model's ability to generalize well is significantly constrained. Additionally, these methods often overlook the inherent uncertainty in the memory data distribution, which differs significantly from the distribution of all previous data examples. To overcome these issues, we propose a principled memory evolution framework that dynamically adjusts the memory data distribution. This evolution is achieved by employing distributionally robust optimization (DRO) to make the memory buffer increasingly difficult to memorize. We consider two types of constraints in DRO: f-divergence and Wasserstein ball constraints. For f-divergence constraint, we derive a family of methods to evolve the memory buffer data in the continuous probability measure space with Wasserstein gradient flow (WGF). For Wasserstein ball constraint, we directly solve it in the euclidean space. Extensive experiments on existing benchmarks demonstrate the effectiveness of the proposed methods for alleviating forgetting. As a by-product of the proposed framework, our method is more robust to adversarial examples than compared CL methods.