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Deep neural network (DNN)-aided spatial modulation (SM) is conceived. In particular, a pair of DNN structures are designed for replacing the conventional model-based channel estimators and detectors. As our first prototype, the conventional DNN estimates the channel relying on the pilot symbols and then carries out data detection in a data-driven manner. By contrast, our new DeepSM scheme is proposed for operation in more realistic time-varying channels, which updates the channel state information (CSI) at each time-slot (TS) before detecting the data. Hence, our novel DeepSM scheme is capable of performing well even in highly dynamic communication environments. Finally, our simulations show that the proposed DeepSM outperforms the conventional model-based channel estimation and data detection for transmission over time-varying channels.