In less than a decade, smartphones and mobile applications spread like wildfire and dramatically improved aspects of our professional and private lives, from efficiency to safety. However, these applications are still in their infancy and mostly provide mobile versions of online Internet services or arcade games. With the exception of simple location-based query applications, context-awareness is largely ignored. However, it is not hard to imagine advanced mobile social networking applications -- SNAPPs for short -- that could proactively assist users in everyday tasks, improving their quality of life. Such services would require massive data collection, processing and communication between mobile devices. Unfortunately, the current centralised communication paradigm represents a major barrier to such intense networking. In this paper, we claim that a fundamental paradigm shift in communication is required to allow such application to see the light of day. The paper claims that such a shift is possible and that it resides in moving towards decentralised communication by taking advantage of the largely untapped network, storage and processing power capabilities offered by idle mobile devices. The paper presents and discusses a number of research questions that must be addressed in order to achieve this paradigm shift.