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Future smart grid systems will intelligently monitor and control energy flows to improve the efficiency and reliability of power delivery. This monitoring and control requires low-delay, highly reliable communication between customers, local utilities, and regional utilities. A vital part of future smart grids is the two way communication links between smart meters at the customer sites and a (decentralized) command and control center operated by the local utility. To enable these two-way communication links, narrowband power line communication (PLC) systems operating in the 3-500 kHz band are attractive because they can be deployed over existing outdoor power lines. Power lines, however, have traditionally been designed for one-directional power delivery and remain hostile environments for communication signal propagation. In this article, we review signal processing approaches to model channel impairments and impulsive noise and mitigate their effects in narrowband PLC systems. We examine ways to improve the communication performance based on current and emerging standards.