The 5G cellular wireless systems will have a multi-tier architecture consisting of macrocells, different types of licensed small cells and D2D networks to serve users with different quality-of-service (QoS) requirements in a spectrum efficient manner. Distributed resource allocation and interference management is one of the fundamental research challenges for such multi-tier heterogeneous networks. In this chapter, we consider the radio resource allocation problem in a multi-tier orthogonal frequency division multiple access (OFDMA)-based cellular (e.g., 5G LTE-A) network. In particular, we present three novel approaches for distributed resource allocation in such networks utilizing the concepts of stable matching, factor-graph based message passing, and distributed auction. We illustrate each of the modeling schemes with respect to a practical radio resource allocation problem. In particular, we consider a multi-tier network consisting a macro base station (MBS), a set of small cell base stations (SBSs) and corresponding small cell user equipments (SUEs), as well as D2D user equipments (DUEs). There is a common set of radio resources (e.g., resource blocks [RBs]) available to the network tiers (e.g., MBS, SBSs and DUEs). The SUEs and DUEs use the available resources (e.g., RB and power level) in an underlay manner as long as the interference caused to the macro tier (e.g., macro user equipments [MUEs]) remains below a given threshold. Followed by a brief theoretical overview of the modeling tools (e.g., stable matching, message passing and auction algorithm), we present the distributed solution approaches for the resource allocation problem in the aforementioned network setup. We also provide a brief qualitative comparison in terms of various performance metrics such as complexity, convergence, algorithm overhead etc.