Numerous surveillance pathways sculpt eukaryotic transcriptomes by degrading unneeded, defective, and potentially harmful noncoding RNAs (ncRNAs). Because aberrant and excess ncRNAs are largely degraded by exoribonucleases, a key characteristic of these RNAs is an accessible, protein-free 5' or 3' end. Most exoribonucleases function with cofactors that recognize ncRNAs with accessible 5' or 3' ends and/or increase the availability of these ends. Noncoding RNA surveillance pathways were first described in budding yeast, and there are now high-resolution structures of many components of the yeast pathways and significant mechanistic understanding as to how they function. Studies in human cells are revealing the ways in which these pathways both resemble and differ from their yeast counterparts, and are also uncovering numerous pathways that lack equivalents in budding yeast. In this review, we describe both the well-studied pathways uncovered in yeast and the new concepts that are emerging from studies in mammalian cells. We also discuss the ways in which surveillance pathways compete with chaperone proteins that transiently protect nascent ncRNA ends from exoribonucleases, with partner proteins that sequester these ends within RNPs, and with end modification pathways that protect the ends of some ncRNAs from nucleases.