This tutorial is concerned with various aspects of component-based design and compositional analysis of real-time embedded systems. It will first give an overview of component-based frameworks and their underlying principles. It will then go in-depth into abstraction methods for real-time components and techniques for computing their optimal interfaces, for both systems implemented on uniprocessor and multiprocessor platforms, as well as extensions to multi-mode systems. Besides theoretical aspects, the tutorial will also present an implementation of the compositional analysis framework on Xen virtualization and a demonstration of the CARTS toolset with several examples seeing the techniques in action. It will also include two case studies highlighting the utility of the framework, including the ARINC-653 avionics software and a smart-phone application. We will conclude the tutorial with a number of open challenges and research opportunities in this domain.