The advent of tau-targeted PET tracers such as flortaucipir (18F) (flortaucipir, also known as 18F-AV-1451 or 18F-T807) have made it possible to investigate the sequence of development of tau in relationship to age, amyloid-β, and to the development of cognitive impairment due to Alzheimer's disease. Here we report a multicentre longitudinal evaluation of the relationships between baseline tau, tau change and cognitive change, using flortaucipir PET imaging. A total of 202 participants 50 years old or older, including 57 cognitively normal subjects, 97 clinically defined mild cognitive impairment and 48 possible or probable Alzheimer's disease dementia patients, received flortaucipir PET scans of 20 min in duration beginning 80 min after intravenous administration of 370 MBq flortaucipir (18F). On separate days, subjects also received florbetapir amyloid PET imaging, and underwent a neuropsychological test battery. Follow-up flortaucipir scans and neuropsychological battery assessments were also performed at 9 and 18 months. Fifty-five amyloid-β+ and 90 amyloid-β- subjects completed the baseline and 18-month study visits and had valid quantifiable flortaucipir scans at both time points. There was a statistically significant increase in the global estimate of cortical tau burden as measured by standardized uptake value ratio (SUVr) from baseline to 18 months in amyloid-β+ but not amyloid-β- subjects (least squared mean change in flortaucipir SUVr : 0.0524 ± 0.0085, P < 0.0001 and 0.0007 ± 0.0024 P = 0.7850, respectively), and a significant association between magnitude of SUVr increase and baseline tau burden. Voxel-wise evaluations further suggested that the regional pattern of change in flortaucipir PET SUVr over the 18-month study period (i.e. which regions exhibited the greatest change) also varied as a function of baseline global estimate of tau burden. In subjects with lower global SUVr, temporal lobe regions showed the greatest flortaucipir retention, whereas in subjects with higher baseline SUVr, parietal and frontal regions were increasingly affected. Finally, baseline flortaucipir and change in flortaucipir SUVr were both significantly (P < 0.0001) associated with changes in cognitive performance. Taken together, these results provide a preliminary characterization of the longitudinal spread of tau in Alzheimer's disease and suggest that the amount and location of tau may have implications both for the spread of tau and the cognitive deterioration that may occur over an 18-month period.