Sensing cost and data quality are two primary concerns in mobile crowdsensing. In this article, we propose a new crowdsensing paradigm, sparse mobile crowdsensing, which leverages the spatial and temporal correlation among the data sensed in different sub-areas to significantly reduce the required number of sensing tasks allocated, thus lowering overall sensing cost (e.g., smartphone energy consumption and incentives) while ensuring data quality. Sparse mobile crowdsensing applications intelligently select only a small portion of the target area for sensing while inferring the data of the remaining unsensed area with high accuracy. We discuss the fundamental research challenges in sparse mobile crowdsensing, and design a general framework with potential solutions to the challenges. To verify the effectiveness of the proposed framework, a sparse mobile crowdsensing prototype for temperature and traffic monitoring is implemented and evaluated. With several future research directions identified in sparse mobile crowdsensing, we expect that more research interests will be stimulated in this novel crowdsensing paradigm