In this paper we compare EUV Imaging Telescope (EIT) waves with simultaneous phenomena seen in H in order to address the question of what an EIT wave is. We surveyed the events associated with solar flares larger than GOES M-class in 1999-2002. The H data are taken with the Flare-monitoring Telescope (FMT) at the Hida Observatory of Kyoto University. Among 14 simultaneous observations of EIT waves and H, 11 were found to have filament eruptions, three were associated with Moreton waves, and one was found to have only filament oscillations. This shows that we cannot see clear wave fronts in H even if EIT waves exist, but that it is possible to recognize invisible waves by means of filament oscillations. The nature of filament oscillations and Moreton waves associated with EIT waves is examined in detail, and it is found that the filament oscillations were caused by EIT waves.