The field of large language models (LLMs) is moving towards addressing the challenge of catastrophic forgetting in continual learning. Researchers are exploring innovative strategies to mitigate this issue, including model growth, parameter-efficient fine-tuning, and novel pruning methods. These approaches aim to improve the retention of previously learned capabilities while adapting to new tasks and domains. Noteworthy papers in this area include: Mitigating Catastrophic Forgetting in Continual Learning through Model Growth, which explores the use of model growth to structure the training of larger models. Forward-Only Continual Learning, which proposes a forward-only, gradient-free continual learning method. LAMDAS: LLM as an Implicit Classifier for Domain-specific Data Selection, which introduces a novel approach to strategic data selection using the pre-trained LLM as an implicit classifier. Mitigating Catastrophic Forgetting in Large Language Models with Forgetting-aware Pruning, which proposes a novel pruning-based approach to balance catastrophic forgetting and downstream task performance.