ABSTRACT Ordered assembly of the tau protein into filaments characterizes multiple neurodegenerative diseases, which are called tauopathies. We previously reported that by electron cryo-microscopy (cryo-EM), tau filament structures from Alzheimer’s disease (1,2), chronic traumatic encephalopathy (CTE) (3), Pick’s disease (4) and corticobasal degeneration (CBD) (5) are distinct. Here we show that the structures of tau filaments from typical and atypical progressive supranuclear palsy (PSP), the most common tauopathy after Alzheimer’s disease, define a previously unknown, three-layered fold. Moreover, the tau filament structures from globular glial tauopathy (GGT, Types I and II) are similar to those from PSP. The tau filament fold of argyrophilic grain disease (AGD) differs from the above and resembles the four-layered CBD fold. The majority of tau filaments from aging-related tau astrogliopathy (ARTAG) also have the AGD fold. Surprisingly, tau protofilament structures from inherited cases with mutations +3/+16 in intron 10 of MAPT , the microtubule-associated protein tau gene, are identical to those from AGD, suggesting that a relative overproduction of four-repeat tau can give rise to the AGD fold. Finally, tau filament structures from cases of familial British dementia (FBD) and familial Danish dementia (FDD) are the same as those from Alzheimer’s disease and primary age-related tauopathy (PART). These structures provide the basis for a classification of tauopathies that also allows identification of new entities, as we show here for a case diagnosed as PSP, but with abundant spherical 4R tau inclusions in limbic and other brain areas. The structures of the tau fold of this new disease (Limbic-predominant Neuronal inclusion body 4R Tauopathy, LNT) were intermediate between those of GGT and PSP.