The architecture of cellular networks has been undergoing an extraordinarily fast evolution in the last years to keep up with the ever increasing user demands for wireless data and services. Motivated by a search for a breakthrough in network capacity, the paradigm of heterogeneous networks (HetNets) has become prominent in modern cellular systems, where carefully deployed macrocells coexist with layers of irregularly deployed cells of reduced coverage sizes. Users can thus be offloaded from the macrocell and the capacity of the network increases. However, universal frequency reuse is usually employed to maximize capacity gains, thereby introducing the fundamental problem of inter-cell interference (ICI) in the network caused by the sharing of the spectrum among the different tiers of the HetNet. The objective of this PhD thesis is to provide analysis and mitigation techniques for the fundamental problem of interference in heterogeneous cellular networks. First, the interference of a two-tier network is modeled and analyzed by making use of spatial statistics tools that allow the reconstruction of complete coverage maps. A correlation analysis is then performed by deriving a spatial coverage cross-tier correlation function. Second, a novel architecture design is proposed to minimize interference in HetNets whose base stations may be equipped with very large antenna arrays, another key technology of future wireless systems. Then, we present interference mitigation techniques for different types of small cells, namely picocells and femtocells. In the third contribution of this thesis, we analyze the case of clustered deployments by proposing and comparing techniques suitable for this scenario. Fourth, we tackle the case of femtocell deployments by analyzing the degrading effect of interference and proposing new mitigation methods. Fifth, we introduce femtorelays, a novel small cell access technology that combats interference in femtocell networks and provides higher backhaul capacity.