  Recent experimental and theoretical results on kaon semileptonic decays have
significantly improved the determination of the CKM matrix element V_us. After
briefly summarizing the impact of the new experimental determinations, I will
concentrate in this talk on the theoretical progresses, coming in particular
from lattice QCD calculations. These results lead to the estimate |V_us|=0.2250
+- 0.0021, in good agreement with the expectation based on the determination of
|V_ud| and the unitarity of the CKM matrix.
