Conventional beamforming methods for intelligent reflecting surfaces (IRSs) or reconfigurable intelligent surfaces (RISs) typically entail the full channel state information (CSI). However, the computational cost of channel acquisition soars exponentially with the number of IRSs. To bypass this difficulty, we propose a novel strategy called blind beamforming that coordinates multiple IRSs by means of statistics without knowing CSI. Blind beamforming only requires measuring the received signal power at the user terminal for a sequence of randomly generated phase shifts across all IRSs. The main idea is to extract the key statistical quantity for beamforming by exploring only a small portion of the whole solution space of phase shifts. We show that blind beamforming guarantees a signal-to-noise ratio (SNR) boost of Θ(N 2L ) under certain conditions, where L is the number of IRSs and N is the number of reflecting elements per IRS. The above result significantly improves upon the state of the art in the area of multi-IRS assisted communication. Moreover, blind beamforming is justified via field tests and simulations.Index Terms-Intelligent reflecting surface (IRS), reconfigurable intelligent surface (RIS), multi-IRS/RIS systems, blind beamforming without channel state information (CSI).