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Device-to-device (D2D) communications allow direct communications between nodes without transmitting data via the base stations in cellular systems, which could bring significant performance improvement. Since most applications are delay-sensitive, it is very important to consider delay performance in addition to physical layer throughput for D2D communications. To improve delay performance it is necessary to dynamically control the radio resource in a cross-layer way according to both the channel fading information and the queue length information. The former allows an observation of good transmission opportunity and the latter provides the urgency of data flows. However, the resource control with delay constraints involves stochastic optimization, which is very challenging. In this article we first summarize various approaches to solve the delay-aware resource allocation problems for D2D communications. We propose a low complexity practical solution by exploiting the interference filtering property of CSMA-like MAC protocols in the D2D system. Based on the solution structure, we further discuss the implementation issues based on LTE-Advanced systems and evaluate the associated performance and complexity. Finally we discuss the choice of MAC parameters for the overall D2D system performance.