Nowadays, big data analytics in genomics is an emerging research topic. In fact, the large amount of genomics data originated by emerging next-generation sequencing (NGS) techniques requires more and more fast and sophisticated algorithms. In this context, deep learning is re-emerging as a possible approach to speed up the DNA sequencing process. In this review, we specifically discuss such a trend. In particular, starting from an analysis of the interest of the Internet community in both NGS and deep learning, we present a taxonomic analysis highlighting the major software solutions based on deep learning algorithms available for each specific NGS application field. We discuss future challenges in the perspective of cloud computing services aimed at deep learning based solutions for NGS.