The production of cellular RNAs is tightly regulated to ensure gene expression is limited to appropriate times and locations. Elimination of RNA can be rapid and programmed to quickly terminate gene expression, or can be used to purge old, damaged or inappropriately formed RNAs. It is elimination of RNAs through the action of a polyadenylation complex (TRAMP), first described in the yeast Saccharomyces cerevisiae, which is the focus of this review. The discovery of TRAMP and presence of orthologs in most eukaryotes, along with an increasing number of potential TRAMP substrates in the form of new small non-coding RNAs, many of which emanate from areas of genomes once thought transcriptionally silent; promise to make this area of research of great interest for the foreseeable future.