Continuous learning from streaming data is among the most challenging topics in the contemporary machine learning. In this domain, learning algorithms must not only be able to handle massive volumes of rapidly arriving data, but also adapt themselves to potential emerging changes. The phenomenon of the evolving nature of data streams is known as concept drift. While there is a plethora of methods designed for detecting its occurrence, all of them assume that the drift is connected with underlying changes in the source of data. However, one must consider the possibility of a malicious injection of false data that simulates a concept drift. This adversarial setting assumes a poisoning attack that may be conducted in order to damage the underlying classification system by forcing adaptation to false data. Existing drift detectors are not capable of differentiating between real and adversarial concept drift. In this paper, we propose a framework for robust concept drift detection in the presence of adversarial and poisoning attacks. We introduce the taxonomy for two types of adversarial concept drifts, as well as a robust trainable drift detector. It is based on the augmented Restricted Boltzmann Machine with improved gradient computation and energy function. We also introduce Relative Loss of Robustness - a novel measure for evaluating the performance of concept drift detectors under poisoning attacks. Extensive computational experiments, conducted on both fully and sparsely labeled data streams, prove the high robustness and efficacy of the proposed drift detection framework in adversarial scenarios.