The smart grid is characterized by the two-way flow of electric power and information. For the information flow implementation and support, several wireless communication technologies and standards are being considered. Although there is no doubt that using wireless communications offers significant benefits over wired connections, the wireless technology introduces additional vulnerability in terms of network security. This work addresses physical layer security, a topic that has been hardly investigated in the smart grid domain. To understand new types of threats, we review fundamentals of wireless communication and examine physical attack models in depth. As a promising solution to physical security, we describe a random spread-spectrum based wireless communication scheme that can achieve both fast and robust data transmission. We expect that the work presented here will advance the research on wireless smart grid security.