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Fog computing has enabled the extension of cloud computing functions to the network edge by assisting the cloud and users in terms of communication, computation, and storage with a widely spread deployment of edge devices or fog nodes, as they become more powerful in capacities and functionalities. Smart grid is becoming the next-generation power grid and will automate reliable electricity distribution for millions of customers. However, the data transmitted in smart grid communications has reached the terabyte level and the mishandling of smart meter readings may lead to customers' privacy leakage. In this article, we present an architecture of fog-based smart grid, discuss its applications, security and privacy challenges, and introduce several state-of-the-art works. We also propose a privacy-preserving authentication and data aggregation scheme for fog-based smart grid. Specifically, we use short randomizable signature and blind signature to provide anonymous authentication in a conditional way, and then we utilize fog nodes to solve billing problems after anonymous authentication. Also, we aggregate the smart meter readings by the homomorphic Paillier cryptosystem. Finally, we aim to attract more attention to this emerging topic by giving some interesting future directions. [ABSTRACT FROM AUTHOR]