Docker container update strategies include rolling updates and blue-green deployments. In Docker Swarm, use docker service update --image new_image_name for updates, combined with --update-parallelism (parallel update count), --update-delay (update interval), --update-failure-action (failure handling strategy) parameters for rolling updates. Blue-green deployment requires creating two services (blue and green), achieving zero-downtime updates by switching traffic. Kubernetes provides more powerful update strategies: RollingUpdate, Recreate, OnDelete. Before updating, it's recommended to conduct thorough testing and prepare a rollback plan.