The cercozoan family Heteromitidae comprises morphologically rather uniform gliding zooflagellates, including Bodomorpha and Heteromita, the most ubiquitous and numerous soil protozoa. The generally used name 'Heteromita globosa' for the commonest gliding biflagellates is incorrect. 'Heteromita' Dujardin, 1841 originally contained only two probable euglenozoans and an unidentifiable flagellate, making it inapplicable to Cercozoa. Accordingly, we establish a new order Glissomonadida for Heteromitidae sensu Cavalier-Smith and Chao, 2003. We cultured over 100 glissomonad strains, sequenced their 18S rRNA genes, and studied their behaviour and morphology by differential interference contrast high definition video microscopy. Group-specific amplification and sequencing of over 450 18S rRNA genes from environmental DNA shows that one temperate grassland plot has hundreds of species, there are thousands globally, and tropical species often differ. Glissomonads are probably sisters of Pansomonadida, not Cercomonadida. In a thorough overhaul of glissomonad taxonomy we describe 29 new species, new genera Sandona, Neoheteromita, Flectomonas, Allapsa, and Teretomonas, and morphologically distinctive families: Sandonidae, Allapsidae, Bodomorphidae, and Proleptomonadidae.