Both real-time virtualization and recursive virtualization are desirable properties of a virtual machine monitor (or hypervisor). Although the prospect for virtualization and even recursive virtualization has become better as the PC hardware becomes faster, the real-time systems community so far has not been able to reap much benefits. This is because no existing virtualization mechanism can properly support the stringent timing requirements needed by real-time systems. It is hard to do real-time virtualization, and it is even harder to do it recursively. In this dissertation, we propose a framework whereby the hypervisor is capable of running real-time guests and participating in recursive virtualization. Such a hypervisor is called a real-time hierarchical hypervisor. We first look at virtualization of abstract resource types from the real-time systems perspective. Unlike the previous work on recursive real-time partitioning that assumes fully-preemptable resources, we concentrate on other and often more practical types of scheduling constraints, especially the non-preemptive and limited-preemptive ones. Then we consider the current x86 architecture and explore the problems that need to be addressed for real-time recursive virtualization. We drill down on the problem that affects timing properties the most, namely, the recursive forwarding and delivery of interrupts, exceptions and intercepts. We choose the x86 architecture because it is popular and readily available, but it is by no means the only architecture of choice for real-time recursive virtualization. We conclude the research with an architecture-independent discussion on future possibilities in real-time recursive virtualization. / text