Spoken keyword spotting (KWS) deals with the identification of keywords in audio streams and has become a fast-growing technology thanks to the paradigm shift introduced by deep learning a few years ago. This has allowed the rapid embedding of deep KWS in a myriad of small electronic devices with different purposes like the activation of voice assistants. Prospects suggest a sustained growth in terms of social use of this technology. Thus, it is not surprising that deep KWS has become a hot research topic among speech scientists, who constantly look for KWS performance improvement and computational complexity reduction. This context motivates this paper, in which we conduct a literature review into deep spoken KWS to assist practitioners and researchers who are interested in this technology. Specifically, this overview has a comprehensive nature by covering a thorough analysis of deep KWS systems (which includes speech features, acoustic modeling and posterior handling), robustness methods, applications, datasets, evaluation metrics, performance of deep KWS systems and audio-visual KWS. The analysis performed in this paper allows us to identify a number of directions for future research, including directions adopted from automatic speech recognition research and directions that are unique to the problem of spoken KWS.