One of the most significant biological discoveries of the last decade is represented by the reality that the vast majority of the transcribed genomic output comprises diverse classes of noncoding RNAs (ncRNAs) that may play key roles and/or be affected by many biochemical cellular processes (i.e., RNA editing), with implications in human health and disease. With 90% of the human genome being transcribed and novel classes of ncRNA emerging (tRNA-derived small RNAs and circular RNAs among others), the great majority of the human transcriptome suggests that many important ncRNA functions/processes are yet to be discovered. An approach to filling such vast void of knowledge has been recently provided by the increasing application of next-generation sequencing (NGS), offering the unprecedented opportunity to obtain a more accurate profiling with higher resolution, increased throughput, sequencing depth, and low experimental complexity, concurrently posing an increasing challenge in terms of efficiency, accuracy, and usability of data analysis software. This review provides an overview of ncRNAs, NGS technology, and the most recent/popular computational approaches and the challenges they attempt to solve, which are essential to a more sensitive and comprehensive ncRNA annotation capable of furthering our understanding of this still vastly uncharted genomic territory.