Humans are proficient at continuously acquiring and integrating new knowledge. By contrast, deep models forget catastrophically, especially when tackling highly long task sequences. Inspired by the way our brains constantly rewrite and consolidate past recollections, we propose a novel Bilateral Memory Consolidation (BiMeCo) framework that focuses on enhancing memory interaction capabilities. Specifically, BiMeCo explicitly decouples model parameters into short-term memory module and long-term memory module, responsible for representation ability of the model and generalization over all learned tasks, respectively. BiMeCo encourages dynamic interactions between two memory modules by knowledge distillation and momentum-based updating for forming generic knowledge to prevent forgetting. The proposed BiMeCo is parameter-efficient and can be integrated into existing methods seamlessly. Extensive experiments on challenging benchmarks show that BiMeCo significantly improves the performance of existing continual learning methods. For example, combined with the state-of-the-art method CwD, BiMeCo brings in significant gains of around 2% to 6% while using 2x fewer parameters on CIFAR-100 under ResNet-18.