  We present a complete calculation of the K_{l3} decays K^+ --> pi^0 l^+ nu_l
and K^0 --> pi^- l^+ nu_l to O(p^4, (m_d-m_u) p^2, e^2 p^2) in chiral
perturbation theory with virtual photons and leptons. We introduce the concept
of generalized form factors and kinematical densities in the presence of
electromagnetism, and propose a possible treatment of the real photon emission
in K^+_{l3} decays. We illustrate our results by applying them to the
extraction of the Kobayashi--Maskawa matrix element |V_{us}| from the
experimental K^+_{e3} decay parameters.
