We review the experimental information on the K + d reaction for K + -meson momenta below 800 MeV/c. The data are analysed within the single scattering impulse approximation -utilizing the Jülich kaon-nucleon model -that allows to take into account effects due to the Fermi motion of the nucleons in the deuteron and the final three-body kinematics for the break-up and charge exchange reaction. We discuss the consistency between the data available for the K + d→K + np, K + d→K 0 pp and K + d→K + d reactions and the calculations based on the spectator model formalism.