Continuous spatio-temporal queries have recently received increasing attention due to the abundance of location-aware applications. This paper addresses the Continuous Reverse Nearest Neighbor (CRNN) Query. Given a set of objects O and a query set Q, the CRNN query monitors the exact reverse nearest neighbors of each query point, under the model that both the objects and the query points may move unpredictably. Existing methods for the reverse nearest neighbor (RNN) query either are static or assume a priori knowledge of the trajectory information, and thus do not apply. Related recent work on continuous range query and continuous nearest neighbor query relies on the fact that a simple monitoring region exists. Due to the unique features of the RNN problem, it is non-trivial to even define a monitoring region for the CRNN query. This paper defines the monitoring region for the CRNN query, discusses how to perform initial computation, and then focuses on incremental CRNN monitoring upon updates. The monitoring region according to one query point consists of two types of regions. We argue that the two types should be handled separately. In continuous monitoring, two optimization techniques are proposed. Experimental results prove that our proposed approach is both efficient and scalable.