Two-component systems, composed of a homodimeric histidine kinase (HK) and a response regulator (RR), are major signal transduction devices in bacteria. Typically the signal triggers HK autophosphorylation at one His residue, followed by phosphoryl transfer from the phospho-His to an Asp residue in the RR. Signal extinction frequently involves phospho-RR dephosphorylation by a phosphatase activity of the HK. Our understanding of these reactions and of the determinants of partner specificity among HK-RR couples has been greatly increased by recent crystal structures and biochemical experiments on HK-RR complexes. Cis-autophosphorylation (one subunit phosphorylates itself) occurs in some HKs while trans-autophosphorylation takes place in others. We review and integrate this new information, discuss the mechanism of the three reactions and propose a model for transmembrane signaling by these systems.