Book excerpt: Multi-tier cellular networks have led to a paradigm shift in the deployment of base stations (BSs) where macrocell BSs are overlaid with smaller and lower power BSs such as microcells, picocells, and femtocells. Stochastic geometry has been proven to be an effective tool to capture such heterogeneity and uncertainties in deployment of cellular BSs. In stochastic geometry, random spatial models are used to model multi-tier cellular networks where the locations of BSs is each tier is assumed to be drawn from a point process with the appropriate spatial density. This thesis proposes stochastic geometry-based approaches to analyze, model, and optimize multi-tier cellular networks under several setups and technologies. First, I propose a novel location-aware cross-tier cooperation scheme that aim at improving the performance of users with low signal-to-interference-plus-noise ratio (SINR). Second, I study the performance of cognitive device-to-device (D2D) communication in multi-channel downlink-uplink cellular network with energy harvesting. For the coexistence between cellular and D2D transmissions, I propose a spectrum access policy for cellular BSs to avoid using D2D channels when possible. Third, I investigate the feasibility of energy harvesting from ambient RF interference in multi-tier uplink cellular networks. For this setup, I capture randomness in the network topology and the battery dynamics. Fourth, I extend multi-tier uplink cellular networks to consider the case when users do not necessarily associate with the nearest BS (i.e., flexible cell association). Finally, I compare between different cell association criteria including coupled and decoupled cell association for uplink and downlink transmissions in multi-tier full-duplex cellular networks. For all network setups, I use stochastic geometry to derive simple and closed-form expressions to evaluate the performance in terms of several metrics, e.g., outage probability, mean rate, transmission probability, success probability, and load per BS. I also highlight main tradeoffs in different networks and provide guidelines to optimize different performance metrics by carefully tuning fundamental network design parameters.