Pushing wireless data traffic onto small cells is important for alleviating congestion in the over-loaded macrocellular network. However, the ultimate potential of such load balancing and its effect on overall system performance is not well understood. With the ongoing deployment of multiple classes of access points (APs) with each class differing in transmit power, employed frequency band, and backhaul capacity, the network is evolving into a complex and “organic” heterogeneous network or HetNet. Resorting to system-level simulations for design insights is increasingly prohibitive with such growing network complexity. The goal of this dissertation is to develop realistic yet tractable frameworks to model and analyze load balancing dynamics while incorporating the heterogeneous nature of these networks. First, this dissertation introduces and analyzes a class of user-AP association strategies, called stationary association, and the resulting association cells for HetNets modeled as stationary point processes. A “Feller-paradox”-like relationship is established between the area of the association cell containing the origin and that of a typical association cell. This chapter also provides a foundation for subsequent chapters, as association strategies directly dictate the load distribution across the network. Second, this dissertation proposes a baseline model to characterize downlink rate and signal-to-interference-plus-noise-ratio (SINR) in an M-band K-tier HetNet with a general weighted path loss based association. Each class of APs is modeled as an independent Poisson point process (PPP) and may differ in deployment density, transmit power, bandwidth (resource), and path loss exponent. It is shown that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage. One of the main outcomes is demonstrating the aggressive of- floading required for out-of-band small cells (like WiFi) as compared to those for in-band (like picocells). To achieve aggressive load balancing, the offloaded users often have much lower downlink SINR than they would on the macrocell, particularly in co-channel small cells. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. As the third contribution, this dissertation proposes a tractable framework to analyze joint load balancing and resource partitioning in co-channel HetNets. Fourth, this dissertation investigates the impact of uplink load balancing. Power control and spatial interference correlation complicate the mathixematical analysis for the uplink as compared to the downlink. A novel generative model is proposed to characterize the uplink rate distribution as a function of the association and power control parameters, and used to show the optimal amount of channel inversion increases with the path loss variance in the network. In contrast to the downlink, minimum path loss association is shown to be optimal for uplink rate coverage. Fifth, this dissertation develops a model for characterizing rate distribution in self-backhauled millimeter wave (mmWave) cellular networks and thus generalizes the earlier multi-band offloading framework to the co-existence of current ultra high frequency (UHF) HetNets and mmWave networks. MmWave cellular systems will require high gain directional antennas and dense AP deployments. The analysis shows that in sharp contrast to the interferencelimited nature of UHF cellular networks, mmWave networks are usually noiselimited. As a desirable side effect, high gain antennas yield interference isolation, providing an opportunity to incorporate self-backhauling. For load balancing, the large bandwidth at mmWave makes offloading users, with reliable mmWave links, optimal for rate. / text