Research on Mission-Critical Application Execution in Fog Computing focuses on enabling reliable, low-latency, and secure execution of applications that demand high availability, strict timing constraints, and robust performance at the network edge. This area addresses challenges posed by resource-constrained and heterogeneous fog nodes, dynamic workloads, and the need for real-time decision-making. Key research directions include designing latency-aware and fault-tolerant scheduling and resource allocation algorithms, predictive workload management, and priority-based task execution frameworks for critical applications. Other emerging topics involve QoS- and SLA-aware execution strategies, real-time monitoring and adaptive control for reliability, secure and resilient fog infrastructure for critical workloads, and edge–fog–cloud collaborative execution models. Additionally, research on energy-efficient execution, container- and microservices-based deployment, and integration with IoT and cyber-physical systems for mission-critical applications represents significant avenues for advancing dependable and efficient fog computing systems.