Model Predictive Control (MPC) is a model-based technique widely and successfully used over the past years to improve control systems performance. A key factor prohibiting the widespread adoption of MPC for complex systems such as buildings is related to the difficulties (cost, time and effort) associated with the identification of a predictive model of a building. To overcome this problem, we introduce a novel idea for predictive control based on historical building data leveraging machine learning algorithms like regression trees and random forests. We call this approach Data-driven model Predictive Control (DPC), and we apply it to three different case studies to demonstrate its performance, scalability, and robustness. In the first case study we consider a benchmark MPC controller using a bilinear building model, then we apply DPC to a data-set simulated from such bilinear model and derive a controller based only on the data. Our results demonstrate that DPC can provide comparable performance with respect to MPC applied to a perfectly known mathematical model. In the second case study, we apply DPC to a 6 story 22 zone building model in EnergyPlus, for which model-based control is not economical and practical due to extreme complexity, and address a Demand Response problem. Our results demonstrate scalability and efficiency of DPC showing that DPC provides the desired power curtailment with an average error of 3%. In the third case study, we implement and test DPC on real data from an off-grid house located in L’Aquila, Italy. We compare the total amount of energy saved with respect to the classical bang-bang controller, showing that we can perform an energy saving up to 49.2%. Our results demonstrate the robustness of our method to uncertainties both in real data acquisition and weather forecast.