Heterokonts are evolutionarily important as the most nutritionally diverse eukaryote supergroup and the most species-rich branch of the eukaryotic kingdom Chromista. Ancestrally photosynthetic/phagotrophic algae (mixotrophs), they include several ecologically important purely heterotrophic lineages, all grossly understudied phylogenetically and of uncertain relationships. We sequenced 18S rRNA genes from 14 phagotrophic non-photosynthetic heterokonts and a probable Ochromonas, performed phylogenetic analysis of 210–430 Heterokonta, and revised higher classification of Heterokonta and its three phyla: the predominantly photosynthetic Ochrophyta; the non-photosynthetic Pseudofungi; and Bigyra (now comprising subphyla Opalozoa, Bicoecia, Sagenista). The deepest heterokont divergence is apparently between Bigyra, as revised here, and Ochrophyta/Pseudofungi. We found a third universal heterokont signature sequence, and deduce three independent losses of ciliary hairs, several of 1-2 cilia, 10 of photosynthesis, but perhaps only two plastid losses. In Ochrophyta, heterotrophic Oikomonas is sister to the photosynthetic Chrysamoeba, whilst the abundant freshwater predator Spumella is biphyletic; neither clade is specifically related to Paraphysomonas, indicating four losses of photosynthesis by chrysomonads. Sister to Chrysomonadea (Chrysophyceae) is Picophagea cl. nov. (Picophagus, Chlamydomyxa). The diatom-parasite Pirsonia belongs in Pseudofungi. Heliozoan-like actinophryids (e.g. Actinosphaerium) are Opalozoa, not related to pedinellids within Hypogyristea cl. nov. of Ochrophyta as once thought. The zooflagellate class Bicoecea (perhaps the ancestral phenotype of Bigyra) is unexpectedly diverse and a major focus of our study. We describe four new biciliate bicoecean genera and five new species: Nerada mexicana, Labromonas fenchelii (=Pseudobodo tremulans sensu Fenchel), Boroka karpovii (=P. tremulans sensu Karpov), Anoeca atlantica and Cafeteria mylnikovii; several cultures were previously misidentified as Pseudobodo tremulans. Nerada and the uniciliate Paramonas are related to Siluania and Adriamonas; this clade (Pseudodendromonadales emend.) is probably sister to Bicosoeca. Genetically diverse Caecitellus is probably related to Anoeca, Symbiomonas and Cafeteria (collectively Anoecales emend.). Boroka is sister to Pseudodendromonadales/Bicoecales/Anoecales. Placidiales are probably divergent bicoeceans (the GenBank Placidia sequence is a basidiomycete/heterokont chimaera). Two GenBank ‘opalinid’ sequences are fungal; Pseudopirsonia is cercozoan; two previous GenBank ‘Caecitellus’ sequences are Adriamonas.