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Device-to-device communication underlaying a cellular network is a promising technology in future wireless networks to improve network capacity and user experience. While D2D communication has great potential to improve wireless system spectral and energy efficiency due to the proximity of communication parties and higher spectrum reuse gain, tremendous work is still ongoing to turn the promising technology into a reality. This article discusses D2D technical challenges as well as standards progress and important research aspects that enable D2D communications underlaying cellular networks. The key research areas addressed include interference management, multihop D2D communications, and D2D communications in heterogeneous networks. When enabling D2D communications underlaying cellular networks, D2D communications can use either cellular downlink or cellular uplink resources. The two resource sharing modes will create different interference scenarios. The performance evaluation on D2D communications underlaying cellular networks under these two different scenarios is provided.