Theory predicts that an accreting supermassive black hole binary (SMBHB) could be observed as an active galactic nucleus (AGN) that periodically varies in luminosity on the order of its orbital timescale, due to mechanisms such as binary-modulated accretion and relativistic Doppler boost. Several studies have searched for periodically varying quasars as possible SMBHBs in optical time domain surveys, but this signature remains largely unexplored in the X-ray regime. I will discuss our recent search for periodic AGN in the Swift Burst Alert Telescope data set, which is the first systematic study of the hard X-ray variability signature of SMBHBs. I will also discuss the detectability of SMBHBs and the more fruitful search strategy in the context of the eROSITA survey. The discovery of such systems would be of high significance in this new era of multi-messenger astronomy, as they are the possible EM counterparts of nanohertz gravitational-wave sources for the pulsar timing array experiments.