This paper presents a study on modeling and verifying the kernel of Real-Time Operating Systems (RTOS). The study will show advances in formally verifying such an RTOS both by refinement and by model checking approaches. This work fits in the context of Hoare’s verification challenge. Several real-time operating systems will be discussed including some commercial ones. The focus of the latter part of the paper will be on verifying FreeRTOS. The paper investigates a number of ways to verify this operating system. A preliminary set-up of verifying FreeRTOS using model checking is presented.