Introns are removed from precursor messenger RNAs in the cell nucleus by a large ribonucleoprotein complex called the spliceosome. The spliceosome contains five subcomplexes called snRNPs, each with one RNA and several protein components. Interactions of the snRNPs with each other and the intron are highly dynamic, changing in an ordered progression throughout the splicing process. This allosteric cascade of interactions is programmed into the RNA and protein components of the spliceosome, and is driven by a family of DExD/H-box RNA-dependent ATPases. The dependence of cascade progression on multiple intron-recognition events likely serves to enforce the accuracy of splicing. Here, the progression of the allosteric cascade from the first recognition event to the first catalytic step of splicing is reviewed.