The exponential dissemination of proximity computing devices (smartphones, tablets, nanocomputers, etc.) raises important questions on how to transmit, store and analyze data in networks integrating those devices. New approaches like edge computing aim at delegating part of the work to devices in the “edge” of the network. In this article, the focus is on the use of pervasive grids to implement edge computing and leverage such challenges, especially the strategies to ensure data proximity and context awareness, two factors that impact the performance of big data analyses in distributed systems. This article discusses the limitations of traditional big data computing platforms and introduces the principles and challenges to implement edge computing over pervasive grids. Finally, using CloudFIT, a distributed computing platform, the authors illustrate the deployment of a real geophysical application on a pervasive network.