The TADPOLE Challenge compares the performance of algorithms at predicting the future evolution of individuals at risk of Alzheimers disease. TADPOLE Challenge participants train their models and algorithms on historical data from the Alzheimers Disease Neuroimaging Initiative (ADNI) study. Participants are then required to make forecasts of three key outcomes for ADNI-3 rollover participants: clinical diagnosis, ADAS-Cog 13, and total volume of the ventricles -- which are then compared with future measurements. Strong points of the challenge are that the test data did not exist at the time of forecasting (it was acquired afterwards), and that it focuses on the challenging problem of cohort selection for clinical trials by identifying fast progressors. The submission phase of TADPOLE was open until 15 November 2017; since then data has been acquired until April 2019 from 219 subjects with 223 clinical visits and 150 Magnetic Resonance Imaging (MRI) scans, which was used for the evaluation of the participants predictions. Thirty-three teams participated with a total of 92 submissions. No single submission was best at predicting all three outcomes. For diagnosis prediction, the best forecast (team Frog), which was based on gradient boosting, obtained a multiclass area under the receiver-operating curve (MAUC) of 0.931, while for ventricle prediction the best forecast (team EMC1), which was based on disease progression modelling and spline regression, obtained mean absolute error of 0.41% of total intracranial volume (ICV). For ADAS-Cog 13, no forecast was considerably better than the benchmark mixed effects model (BenchmarkME), provided to participants before the submission deadline. Further analysis can help understand which input features and algorithms are most suitable for Alzheimers disease prediction and for aiding patient stratification in clinical trials.