It’s likely a myth that Rasputin was sleeping with the czarina. (Although there’s no proof either way.) He had a very close relationship with the czar and czarina because their son had hemophilia, and Rasputin’s presence seemed to help his condition. It was a serious illness, and the parents were desperate for anything that could help. But the hemophilia was a secret so nobody outside the family knew why the czar and czarina kept Rasputin so close despite dangerous rumours that Rasputin was the one running Russian policy. The idea that Rasputin was sleeping with the czarina was a popular theory because Rasputin was a well-known horny motherfucker.