Cloud Computing provides on-demand computing services like software, networking, storage, analytics, and intelligence over the Internet (“the cloud”). But it is facing challenges because of the explosion of the Internet of Things (IoT) devices and the volume, variety, veracity and velocity of the data generated by these devices. There is a need for ultra-low latency, reliable service along with security and privacy. Fog Computing is a promising solution to overcome these challenges. The originality, scope and novelty of this paper is the definition and formulation of the problem of smart neighborhoods in context of smart grids. This is achieved through an extensive literature study, firstly on Fog Computing and its foundation technologies, its applications and the literature review of Fog Computing research in various application domains. Thereafter, we introduce smart grid and community MicroGrid concepts and, their challenges to give the in depth background of the problem and hence, formalize the problem. The smart grid, which ensures reliable, secure, and cost-effective power supply to the smart neighborhoods, effectively needs Fog Computing architecture to achieve its purpose. This paper also identifies, without rigorous analysis, potential solutions to address the problem of smart neighborhoods. The challenges in the integration of Fog Computing and smart grids are also discussed.