Resonances play a unique role in the study of ultra-relativistic heavy-ion collisions. Resonance yields, which may be modified by rescattering and regeneration after hadronization, can be used to study the properties of the hadronic phase of the collision. The transversemomentum spectra of the proton and the φ(1020) can be used to study the mechanisms of particle production. In addition, resonance measurements in pp and p–Pb collisions help to distinguish initial-state effects from the effects of the hot and dense final state. The ALICE Collaboration has studied the K ∗ (892) 0 and φ(1020) mesons in pp, p–Pb, and Pb–Pb collisions. Measurements of many resonance properties, including pT spectra, integrated yields, masses, widths, mean pT values, and the nuclear modification factors RAA and RpPb, are presented and compared to measurements from other experiments, non-resonances, and the predictions of theoretical models. In relativistic heavy-ion collisions, strongly interacting matter is studied under extreme conditions. Based on quantum chromodynamics (QCD), it is expected that when hadronic matter reaches a high enough energy density a transition will occur in which quarks become deconfined [1–3]. In this state of matter, the quark-gluon plasma (QGP), the relevant degrees of freedom are not hadrons, but rather quarks and gluons. For low baryochemical potentials (typical of heavy-ion collisions at the LHC), the transition between hadronic matter and the QGP is expected to occur around a temperature of Tc ≈ 160 MeV [3–5]. Experimentally, this is achieved by colliding nuclei at