We have constrained unparticle interactions with neutrinos and electrons using available data on neutrino-electron elastic scattering and the four CERN LEP experiments data on mono photon production. We have found that, for neutrino-electron elastic scattering, the MUNU experiment gives better constraints than previous reported limits in the region d>1.5. The results are compared with the current astrophysical limits, pointing out the cases where these limits may or may not apply. We also discuss the sensitivity of future experiments to unparticle physics. In particular, we show that the measurement of coherent reactor neutrino scattering off nuclei could provide a good sensitivity to the couplings of unparticle interaction with neutrinos and quarks. We also discuss the case of future neutrino-electron experiments as well as the International Linear Collider.