In this paper, resource allocation and interference mitigation are investigated for heterogeneous networks where the lowest tier consists of device-to-device (D2D) cells. In order to alleviate dead-zone problem, we first consider downlink/uplink (DL/UL) decoupling user association and quantify its capability on interference management and network-wide D2D performance enhancement. Second, we propose an UL fractional frequency reuse scheme where subband (SB) bandwidths are adaptively determined based on: 1) user equipment (UE) density; 2) e-node-B (eNB) density; and 3) on/off switching frequency of small cells. Obtained results show that the adaptive method significantly reduces the number of outage users. Thereafter, a novel concatenated bi-partite matching (CBM) method is proposed for joint SB assignment (SA) and resource block allocation (RA) of cellular UEs. Numerical results show that the CBM provides a close performance to exhaustive solution with greatly reduced running time. The CBM is then extended to a centralized mode selection, SA, and RA for D2D cells. Alternatively, we develop offline and online semi-distributed approaches where a D2D-cell can reuse white-list RBs (WRBs), which are not occupied by the adjacent small cells. In the former, D2D-cell members are not aware of intra-cell and inter-cell interference and uniformly distribute their maximum permissible power to WRBs. In the latter, we put D2D sum rate maximization into a convex form by exploiting the proximity gain of D2D UEs. Online distributed solution is then developed by message passing of dual variables and consistency prices. Finally, virtues and drawbacks of the developed approaches are compared and explained.