This paper highlights vulnerabilities of deep learning-driven semantic communications to backdoor (Trojan) attacks. Semantic communications aims to convey a desired meaning while transferring information from a transmitter to its receiver. An encoder-decoder pair that is represented by two deep neural networks (DNNs) as part of an autoencoder is trained to reconstruct signals such as images at the receiver by transmitting latent features of small size over a limited number of channel uses. In the meantime, another DNN of a semantic task classifier at the receiver is jointly trained with the autoencoder to check the meaning conveyed to the receiver. The complex decision space of the DNNs makes semantic communications susceptible to adversarial manipulations. In a backdoor (Trojan) attack, the adversary adds triggers to a small portion of training samples and changes the label to a target label. When the transfer of images is considered, the triggers can be added to the images or equivalently to the corresponding transmitted or received signals. In test time, the adversary activates these triggers by providing poisoned samples as input to the encoder (or decoder) of semantic communications. The backdoor attack can effectively change the semantic information transferred for the poisoned input samples to a target meaning. As the performance of semantic communications improves with the signal-to-noise ratio and the number of channel uses, the success of the backdoor attack increases as well. Also, increasing the Trojan ratio in training data makes the attack more successful. In the meantime, the effect of this attack on the unpoisoned input samples remains limited. Overall, this paper shows that the backdoor attack poses a serious threat to semantic communications and presents novel design guidelines to preserve the meaning of transferred information in the presence of backdoor attacks.