The trigger system of a typical multi-purpose LHC experiment needs to process events in real time and select the ~1000 events/sec to be stored for further studies. The short latency limits the complexity of the algorithms used to take decisions. We discuss how deep neural networks could be used as low-latency approximations of complex algorithms and how they could be compressed and optimized to be deployed on the trigger system of a typical experiment, and in particular on the FPGA boards mounted on the first-level trigger electronics. In addition, we show how cloud resources could be used for on-demand deep-learning inference for on-line and off-line processing at future colliders.