Efficient resource management and scheduling have been persistent challenges since the early days of computing and remain crucial today. The widespread adoption of containers managed by orchestrators like Kubernetes has introduced new dimensions to these challenges. Despite their lightweight nature, containers still suffer from inefficiencies due to over-provisioning and long-running workloads allocating resources potentially forever. Existing scheduling techniques are not enough to meet these demands, and there is a growing need for orchestration and scheduling policies that support advanced preemption, migration, and fault tolerance. Well-established container Checkpoint/Restore (C/R) mechanisms, implemented through tools like CRIU, offer a promising solution for improving resource scheduling efficiency. However, these mechanisms remain only partially integrated with Kubernetes. In this paper, we propose a novel Interruption-Aware Scheduling Strategy that incorporates transparent C/R with the Kubernetes scheduler. We discuss the current C/R mechanisms, outline the key design choices involved in integrating with the Kubernetes scheduler, and explore associated challenges and open problems. We further discuss potential solutions to these challenges, offering a path toward more efficient resource management to better meet the needs of today’s computational landscape.