This paper investigates poisoning attacks against data-driven control methods. This work is motivated by recent trends showing that, in supervised learning, slightly modifying the data in a malicious manner can drastically deteriorate the prediction ability of the trained model. We extend these analyses to the case of data-driven control methods. Specifically, we investigate how a malicious adversary can poison the data so as to minimize the performance of a controller trained using this data. We show that identifying the most impactful attack boils down to solving a bi-level non-convex optimization problem, and provide theoretical insights on the attack. We present a generic algorithm finding a local optimum of this problem and illustrate our analysis in the case of a model-reference based approach, the Virtual Reference Feedback Tuning technique, and on data-driven methods based on Willems et al. lemma. Numerical experiments reveal that minimal but well-crafted changes in the dataset are sufficient to deteriorate the performance of data-driven control methods significantly, and even make the closed-loop system unstable.