Tau assembly propagation from the extracellular to intracellular space of a cell may underlie neurodegenerative tauopathies. The first step involves tau binding to heparan sulfate proteoglycans on the cell surface, followed by macropinocytosis. Pathological tau assemblies are thought to exit the vesicular compartment as seeds for replication in the cytoplasm. Tau uptake is highly efficient, but only ~1-10% of cells that take up aggregates exhibit seeding. To investigate the basis for this observation, we used fluorescently tagged full-length (FL) tau fibrils added to native U2OS cells, and biosensor cells expressing FL tau or repeat domain fused to mClover (Clo). FL tau-Clo bound tubulin, but seeds triggered its aggregation in multiple locations simultaneously in the cytoplasm, generally independent of visible exogenous aggregates. Most exogenous tau trafficked to the lysosome, but imaging revealed a small percentage that slowly and steadily accumulated in the cytosol. Intracellular expression of Gal3-mRuby, which binds intravesicular galactosides and forms puncta upon vesicle rupture, revealed no evidence of vesicle damage following tau exposure. In fact, most seeded cells had no evidence of lysosome rupture. However, live cell imaging indicated that cells with pre-existing Gal3-positive puncta exhibited seeding at a slightly higher rate than the general population, indicating a potential role for vesicle instability as a predisposing factor. Clearance of tau seeds occurred rapidly in both vesicular and cytosolic fractions. Bafilomycin inhibited vesicular clearance, whereas MG132 inhibited cytosolic clearance. Tau seeds that enter the cell thus have at least two fates: lysosomal clearance that degrades most tau, and entry into the cytosol, where seeds replicate, and are cleared by the proteasome.