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The machine recognition of speech spoken at a distance from the microphones, known as far-field automatic speech recognition (ASR), has received a significant increase of attention in science and industry, which caused or was caused by an equally significant improvement in recognition accuracy. Meanwhile it has entered the consumer market with digital home assistants with a spoken language interface being its most prominent application. Speech recorded at a distance is affected by various acoustic distortions and, consequently, quite different processing pipelines have emerged compared to ASR for close-talk speech. A signal enhancement front-end for dereverberation, source separation and acoustic beamforming is employed to clean up the speech, and the back-end ASR engine is robustified by multi-condition training and adaptation. We will also describe the so-called end-to-end approach to ASR, which is a new promising architecture that has recently been extended to the far-field scenario. This tutorial article gives an account of the algorithms used to enable accurate speech recognition from a distance, and it will be seen that, although deep learning has a significant share in the technological breakthroughs, a clever combination with traditional signal processing can lead to surprisingly effective solutions.