Eukaryotic genomes are pervasively transcribed. However, it is unclear how many newly found RNAs have functions and how many are byproducts of functional, or spurious, transcription events. Cells control the accumulation of many opportunistic transcripts by limiting their synthesis and by provoking their early transcription termination and decay. In this review, we use S. cerevisiae and mammalian cells as models to discuss the circumstances by which pervasive transcripts are produced and turned over. This ultimately relates to the likelihood, and potential mechanism, of molecular function.