Semantic communications seeks to transfer information from a source while conveying a desired meaning to its destination. We model the transmitter-receiver functionalities as an autoencoder followed by a task classifier that evaluates the meaning of the information conveyed to the receiver. The autoencoder consists of an encoder at the transmitter to jointly model source coding, channel coding, and modulation, and a decoder at the receiver to jointly model demodulation, channel decoding and source decoding. By augmenting the reconstruction loss with a semantic loss, the two deep neural networks (DNNs) of this encoder-decoder pair are interactively trained with the DNN of the semantic task classifier. This approach effectively captures the latent feature space and reliably transfers compressed feature vectors with a small number of channel uses while keeping the semantic loss low. We identify the multi-domain security vulnerabilities of using the DNNs for semantic communications. Based on adversarial machine learning, we introduce test-time (targeted and non-targeted) adversarial attacks on the DNNs by manipulating their inputs at different stages of semantic communications. As a computer vision attack, small perturbations are injected to the images at the input of the transmitter's encoder. As a wireless attack, small perturbations signals are transmitted to interfere with the input of the receiver's decoder. By launching these stealth attacks individually or more effectively in a combined form as a multi-domain attack, we show that it is possible to change the semantics of the transferred information even when the reconstruction loss remains low. These multi-domain adversarial attacks pose as a serious threat to the semantics of information transfer (with larger impact than conventional jamming) and raise the need of defense methods for the safe adoption of semantic communications.