Alzheimer's disease is the most common neurodegenerative disease, and there are no mechanism-based therapies. The disease is defined by the presence of abundant neurofibrillary lesions and neuritic plaques in the cerebral cortex. Neurofibrillary lesions comprise paired helical and straight tau filaments, whereas tau filaments with different morphologies characterize other neurodegenerative diseases. No high-resolution structures of tau filaments are available. Here we present cryo-electron microscopy (cryo-EM) maps at 3.4-3.5 Å resolution and corresponding atomic models of paired helical and straight filaments from the brain of an individual with Alzheimer's disease. Filament cores are made of two identical protofilaments comprising residues 306-378 of tau protein, which adopt a combined cross-β/β-helix structure and define the seed for tau aggregation. Paired helical and straight filaments differ in their inter-protofilament packing, showing that they are ultrastructural polymorphs. These findings demonstrate that cryo-EM allows atomic characterization of amyloid filaments from patient-derived material, and pave the way for investigation of a range of neurodegenerative diseases.