Nuclear RNA processing requires dynamic and intricately regulated machinery composed of multiple enzymes and their cofactors. In this review, we summarize recent experiments using Saccharomyces cerevisiae as a model system that have yielded important insights regarding the conversion of pre-RNAs to functional RNAs, and the elimination of aberrant RNAs and unneeded intermediates from the nuclear RNA pool. Much progress has been made recently in describing the 3D structure of many elements of the nuclear degradation machinery and its cofactors. Similarly, the regulatory mechanisms that govern RNA processing are gradually coming into focus. Such advances invariably generate many new questions, which we highlight in this review.