Flexgrid technology is now considered to be a promising solution for future high-speed network design. In this context, we need a tutorial that covers the key aspects of elastic optical networks. This tutorial paper starts with a brief introduction of the elastic optical network and its unique characteristics. The paper then moves to the architecture of the elastic optical network and its operation principle. To complete the discussion of network architecture, this paper focuses on the different node architectures, and compares their performance in terms of scalability and flexibility. Thereafter, this paper reviews and classifies routing and spectrum allocation (RSA) approaches including their pros and cons. Furthermore, various aspects, namely -fragmentation, modulation, quality-of-transmission, traffic grooming, survivability, energy saving, and networking cost related to RSA, are presented. Finally, the paper explores the experimental demonstrations that have tested the functionality of the elastic optical network, and follows that with the research challenges and open issues posed by flexible networks.Index Terms-Elastic optical networks, node architecture, spectrum management, routing and spectrum allocation, and sliceable bandwidth-variable transponder.