Device-to-Device (D2D) communications and small cell networks, as promising technologies to improve spectral efficiency and system throughput for future cellular networks, have received increasing attentions. In this paper, we model D2D communications in the two-tier heterogeneous macro-small cell networks. We propose not only two novel resource sharing strategies for D2D users, namely dedicated resource sharing strategy and cross-tier resource sharing strategy, but theirs corresponding power control strategies as well. In order to minimize cross-tier interference for the two-tier cellular net...