While semantic communication succeeds in efficiently transmitting due to the strong capability to extract the essential semantic information, it is still far from the intelligent or human-like communications. In this paper, we introduce an essential component, memory, into semantic communications to mimic human communications. Particularly, we investigate a deep learning (DL) based semantic communication system with memory, named Mem-DeepSC, by considering the scenario question answer task. We exploit the universal Transformer based transceiver to extract the semantic information and introduce the memory module to process the context information. Moreover, we derive the relationship between the length of semantic signal and the channel noise to validate the possibility of dynamic transmission. Specially, we propose two dynamic transmission methods to enhance the transmission reliability as well as to reduce the communication overhead by masking some unessential elements, which are recognized through training the model with mutual information. Numerical results show that the proposed Mem-DeepSC is superior to benchmarks in terms of answer accuracy and transmission efficiency, i.e., number of transmitted symbols.