Updating a model over time as the world changes, without retraining from scratch and without it forgetting what it already knew. Both halves are hard, and the honest state of the field is that periodic full retraining remains the practical answer for most organisations.
Technical view
Approaches include regularisation towards previous parameters, rehearsal by mixing in older data, and architectural methods that allocate separate capacity to new tasks. The core difficulty is the stability-plasticity trade-off: resisting change preserves old knowledge and prevents new learning. For large language models, adapter-based approaches with routing avoid touching the base weights, sidestepping rather than solving the problem.
Related
Part of AI Terminology Index, section: Training and Post-training.