While it is well known that 98–99% of the human genome does not encode proteins, but are nevertheless transcriptionally active and give rise to a broad spectrum of noncoding RNAs [ncRNAs] with complex regulatory and structural functions, specific functions have so far been assigned to only a tiny fraction of all known transcripts. On the other hand, the striking observation of an overwhelmingly growing fraction of ncRNAs, in contrast to an only modest increase in the number of protein-coding genes, during evolution from simple organisms to humans, strongly suggests critical but so far essentially unexplored roles of the noncoding genome for human health and disease pathogenesis. Research into the vast realm of the noncoding genome during the past decades thus lead to a profoundly enhanced appreciation of the multi-level complexity of the human genome. Here, we address a few of the many huge remaining knowledge gaps and consider some newly emerging questions and concepts of research. We attempt to provide an up-to-date assessment of recent insights obtained by molecular and cell biological methods, and by the application of systems biology approaches. Specifically, we discuss current data regarding two topics of high current interest: (1) By which mechanisms could evolutionary recent ncRNAs with critical regulatory functions in a broad spectrum of cell types (neural, immune, cardiovascular) constitute novel therapeutic targets in human diseases? (2) Since noncoding genome evolution is causally linked to brain evolution, and given the profound interactions between brain and immune system, could human-specific brain-expressed ncRNAs play a direct or indirect (immune-mediated) role in human diseases? Synergistic with remarkable recent progress regarding delivery, efficacy, and safety of nucleic acid-based therapies, the ongoing large-scale exploration of the noncoding genome for human-specific therapeutic targets is encouraging to proceed with the development and clinical evaluation of novel therapeutic pathways suggested by these research fields.