Hadronic resonances constitute a valuable probe for the properties of the medium formed in heavy-ion collisions. In particular, they provide information on particle-formation mechanisms, the properties of the hadronic medium at freeze-out, and they contribute to the systematic study of energy loss and recombination. The study of resonance production in other collision systems such as pp and p–Pb forms a necessary baseline to disentangle initial-state effects from genuine medium-induced effects. The production of the K⁎(892)0 and ϕ(1020) resonances has been measured at mid-rapidity in different collision systems at LHC energies using the ALICE detector. Resonances are reconstructed via their hadronic decay in a wide momentum range, by exploiting the excellent particle-identification capabilities of the Time-Projection Chamber and the Time-Of-Flight system. First results on K⁎(892)0 and ϕ(1020) production in p–Pb collisions at sNN=5.02 TeV at the LHC are presented. The resonance transverse momentum spectra and yields are measured as a function of the multiplicity of p–Pb collision. Ratios of resonance to long lived hadron production in Pb–Pb are compared with the same quantities measured in pp and p–Pb, in order to investigate rescattering effects. The ratio of ϕ to protons and pions as a function of pT suggests that in central Pb–Pb collisions it is the mass which drives the spectra shapes at low and intermediate pT, as in a hydrodynamically-evolving system. The nuclear modification factors (RAA, RpPb), recently measured up to high pT for resonances, are consistent with those of the stable hadrons.