With the increasing availability of real-time tra?c information, dynamic spatial networks are pervasive nowa-days and path planning in dynamic spatial networks becomes an important issue. In this light, we propose and investigate a novel problem of dynamically monitoring shortest paths in spatial networks (DSPM query). When a traveler aims to a des-tination, his/her shortest path to the destination may change due to two reasons: 1) the travel costs of some edges have been updated and 2) the traveler deviates from the pre-planned path. Our target is to accelerate the shortest path computing in dynamic spatial networks, and we believe that this study may be useful in many mobile applications, such as route planning and recommendation, car navigation and tracking, and location-based services in general. This problem is challenging due to two reasons: 1) how to maintain and reuse the existing computation results to accelerate the following computations, and 2) how to prune the search space effectively. To overcome these challenges, filter-and-refinement paradigm is adopted. We maintain an expansion tree and define a pair of upper and lower bounds to prune the search space. A series of optimization techniques are developed to accelerate the shortest path computing. The performance of the developed methods is studied in extensive experiments based on real spatial data.