The spliceosome is a macromolecular assembly that carries out the excision of introns from nuclear pre-mRNAs. It consists of four large RNA-protein complexes, called the U1, U2, U4/U6 and U5 small nuclear ribonucleoproteins (snRNPs), and many protein factors. Crystal structures of seven protein components and fragments of the U1 and U2 small nuclear RNAs have been determined in the form of RNA-protein and protein-protein complexes. Together with electron microscopy studies of the snRNPs, these structures have begun to provide important insights into the architecture of the snRNPs and the mechanisms of RNA-protein and protein-protein recognition.