Any process in which STAT proteins (Signal Transducers and Activators of Transcription) and JAK (Janus Activated Kinase) proteins convey a signal to trigger a change in the activity or state of a cell. The JAK-STAT cascade begins with activation of STAT proteins by members of the JAK family of tyrosine kinases, proceeds through dimerization and subsequent nuclear translocation of STAT proteins, and ends with regulation of target gene expression by STAT proteins.