Continual learning enables models to learn new tasks sequentially without forgetting previous ones. Challenge: Standard training on new data causes catastrophic forgetting. Model faces stability-plasticity trade-off. Approaches: Regularization-based: EWC (Elastic Weight Consolidation) penalizes changes to important weights, SI (Synaptic Intelligence) tracks parameter importance during training. Replay-based: Store examples from previous tasks (experience replay), generate synthetic samples of old tasks. Architecture-based: Progressive networks add new modules, PackNet prunes and freezes subnetworks per task, modular networks with task-specific routing. For LLMs: Continual pre-training on new domains, instruction tuning without losing base capabilities, mixing old and new data. Evaluation: Forward/backward transfer metrics, average accuracy across all seen tasks. Applications: Models that learn over time in production, personalization without forgetting, adapting to distribution shift. Current research: Rehearsal-free continual learning, continual RLHF, efficient memory management. Critical for deploying AI systems that improve over time without expensive retraining.