Although the use of multiple unmanned aerial vehicles (UAVs) has great potential for fast autonomous exploration, it has received far too little attention. In this article, we present a RApid Collaborative ExploRation (RACER) approach using a fleet of decentralized UAVs. To effectively dispatch the UAVs, a pairwise interaction based on an online hgrid space decomposition is used. It ensures that all UAVs simultaneously explore distinct regions, using only asynchronous and limited communication. Furthermore, we optimize the coverage paths of unknown space and balance the workloads partitioned to each UAV with a capacitated vehicle routing problem formulation. Given the task allocation, each UAV constantly updates the coverage path and incrementally extracts crucial information to support the exploration planning. A hierarchical planner finds exploration paths, refines local viewpoints, and generates minimum-time trajectories in sequence to explore the unknown space agilely and safely. The proposed approach is evaluated extensively, showing high exploration efficiency, scalability, and robustness to limited communication. Furthermore, for the first time, we achieve fully decentralized collaborative exploration with multiple UAVs in the real world. We will release our implementation as an open-source package.