Elastic Optical Network (EON) is an emerging technology that facilitates flexible allocation of fiber spectrum by leveraging finer-grained channel spacing (e.g., 6.25GHz or 12.5GHz), tunable modulation formats (e.g., ranging from BPSK to 128QAM) and Forward Error Correction (FEC) overheads (e.g., 7%, 20%, or even more), and baud-rate assignment (e.g., 28, 47.5, 66 Gbaud/s etc.), to right size spectrum allocation to customer needs. EON virtualization is currently gaining interest, especially because of its importance in future 5G network slicing. A core problem in EON virtualization is to efficiently map a virtual network on the substrate optical network, also known as the Virtual Network Embedding (VNE) problem. VNE has been extensively studied for layer-2/3 electrical and fixed-grid optical networks. However, VNE over EON introduces unique challenges and complexities due to the large number of flexible transmission parameters made available by EONs. In this project, we intend to devise effective and scalable solutions to the VN embedding problem in EON. We will particularly focus on: a) VNE with delay guarantees, b) VNE with differentiated reliability, c) dynamic VNE adaptation in real-time, d) EON VNE re-optimization. Advances in these research avenues in collaboration with our industrial partner Huawei Canada will have a lasting impact on the design principles and management paradigms of the future EONs.