Continual learning algorithms are typically exposed to untrusted sources that contain training data inserted by adversaries and bad actors. An adversary can insert a small number of poisoned samples, such as mislabeled samples from previously learned tasks, or intentional adversarial perturbed samples, into the training datasets, which can drastically reduce the model's performance. In this work, we demonstrate that continual learning systems can be manipulated by malicious misinformation and present a new category of data poisoning attacks specific for continual learners, which we refer to as {\em Poisoning Attacks Against Continual Learners} (PACOL). The effectiveness of labeling flipping attacks inspires PACOL; however, PACOL produces attack samples that do not change the sample's label and produce an attack that causes catastrophic forgetting. A comprehensive set of experiments shows the vulnerability of commonly used generative replay and regularization-based continual learning approaches against attack methods. We evaluate the ability of label-flipping and a new adversarial poison attack, namely PACOL proposed in this work, to force the continual learning system to forget the knowledge of a learned task(s). More specifically, we compared the performance degradation of continual learning systems trained on benchmark data streams with and without poisoning attacks. Moreover, we discuss the stealthiness of the attacks in which we test the success rate of data sanitization defense and other outlier detection-based defenses for filtering out adversarial samples.