The necessity to promote smart grid (SG) has been recognized with a strong consensus. The SG integrates electrical grids and communication infrastructures and forms an intelligent electricity network working with all connected components to deliver sustainable electricity supplies. Many advanced communication technologies have been identified for SG applications with a potential to significantly enhance the overall efficiency of power grids. In this paper, the challenges and applications of communication technologies in SG are discussed. In particular, we identify three major challenges to implement SG communication systems, including standards interoperability, cognitive access to unlicensed radio spectra, and cyber security. The issues to implement SG communications on an evolutional path and its future trends are also addressed. The aim of this paper is to offer a comprehensive review of state-of-the-art researches on SG communications.