Wireless network virtualization (WNV) and millimeter wave (mmW) communications are emerging as two key technologies for cellular networks. Virtualization in cellular networks enables wireless services to be decoupled from network resources (e.g., infrastructure and spectrum) so that multiple virtual networks can be built using a shared pool of network resources. At the same time, utilization of the large bandwidth available in mmW frequency band would help to overcome ongoing spectrum scarcity issues. In this context, this dissertation presents efficient frameworks for building virtual networks in sub-6 GHz and mmW bands. Towards developing the frameworks, first, we derive a closed-form expression for the downlink rate coverage probability of a typical sub-6 GHz cellular network with known base station (BS) locations and stochastic user equipment (UE) locations and channel conditions. Then, using the closed-form expression, we develop a sub-6 GHz virtual resource allocation framework that aggregates, slices, and allocates the sub-6 Ghz network resources to the virtual networks in such a way that the virtual networks' sub-6 GHz downlink coverage and rate demands are probabilistically satisfied while resource over-provisioning is minimized in the presence of uncertainty in UE locations and channel conditions. Furthermore, considering the possibility of lack of sufficient sub-6 GHz resources to satisfy the rate coverage demands of all virtual networks, we design a prioritized sub-6 GHz virtual resource allocation scheme where virtual networks are built sequentially based on their given priorities. To this end, we develop static frameworks that allocate sub-6 GHz resources in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. As a result, when a slice of a BS serves its associated UEs, it can be over-satisfied (i.e., resources left after satisfying the rate demands of all UEs) or under-satisfied (i.e., lack of resources to satisfy the rate demands of all UEs). On the other hand, it is extremely challenging to execute the entire virtual resource allocation process in real time due to the small transmission time intervals (TTIs) of cellular technologies. Taking this into consideration, we develop an efficient scheme that performs the virtual resource allocation in two phases, i.e., virtual network deployment phase (static) and statistical multiplexing phase (adaptive). In the virtual network deployment phase, sub-6 GHz resources are aggregated, sliced, and allocated to the virtual networks considering the presence of uncertainty in UE locations and channel conditions, without knowing which realization of UE locations and channel conditions will occur. Once the virtual networks are deployed, each of the aggregated BSs performs statistical multiplexing, i.e., allocates excess resources from the over-satisfied slices to the under-satisfied slices, according to the realized channel conditions of associated UEs. In this way, we further improve the sub-6 GHz resource utilization. Next, we steer our focus on the mmW virtual resource allocation process. MmW systems typically use beamforming techniques to compensate for the high pathloss. The directional communication in the presence of uncertainty in UE locations and channel conditions, make maintaining connectivity and performing initial access and cell discovery challenging. To address these challenges, we develop an efficient framework for mmW virtual network deployment and UE assignment. The deployment decisions (i.e., the required set of mmW BSs and their optimal beam directions) are taken in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. Once the virtual networks are deployed, an optimal mmW link (or a fallback sub-6 GHz link) is assigned to each UE according to the realized UE locations and channel conditions. Our numerical results demonstrate the gains brought by our proposed scheme in terms of minimizing resource over-provisioning while probabilistically satisfying virtual networks' sub-6 GHz and mmW demands in the presence of uncertainty in UE locations and channel conditions.