Single-cell analyses have revealed a tremendous variety among cells in the abundance and chemical composition of RNA. Much of this heterogeneity is due to alternative splicing by the spliceosome. Little is known about how many of the resulting isoforms are biologically functional or just provide noise with little to no impact. The dynamic nature of the spliceosome provides numerous opportunities for regulation but is also the source of stochastic fluctuations. We discuss possible origins of splicing stochasticity, the experimental approaches for studying heterogeneity in isoforms, and the potential biological significance of noisy splicing in development and disease.