  We discuss the result of a recent quenched lattice calculation of the K -> pi
vector form factor at zero-momentum transfer, relevant for the determination of
|V_us| from K-> pi l nu decays. Using suitable double ratios of three-point
correlation functions, we show that it is possible to calculate this quantity
at the percent-level precision. The leading quenched effects are corrected for
by means of quenched chiral perturbation theory. The final result, f+(0) =
0.960 +- 0.005_stat +- 0.007_syst, turns out to be in good agreement with the
old quark model estimate made by Leutwyler and Roos. In this paper, we discuss
the phenomenological impact of the lattice result for the extraction of |V_us|,
by updating the analysis of K -> pi l nu decays with the most recent
experimental data. We also present a preliminary lattice study of hyperon Sigma
-> n l nu decays, based on a similar strategy.
