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We report on the results of femtoscopic analyses of Pb-Pb collisions at sqrt(s) N N =2.76 TeV and pp collisions at sqrt(s) = 7 TeV with identical charged and neutral kaons. The femtoscopic correlations allow one to measure the space-time characteristics of particle production using particle correlations due to the effects of quantum statistics for identical particles and final state interaction for both identical and non-identical ones. Small contributions from resonance decays make kaon femtoscopy an ideal tool for the correlation studies. In conjunction with pion and proton femtoscopy, they can also reveal properties of collective dynamics in heavy-ion collisions. ALICE results are compared with the existing world data on kaon femtoscopy in different type of collisions. The theoretical expectations for pp and Pb-Pb collisions are considered.