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The production of low-mass dielectrons is one of the most promising tools for the investigation of chiral symmetry restoration and thermal radiation from the QGP created in heavy-ion collisions. To single out the signal characteristics of the QGP, it is crucial to understand the primordial e+e− pair production in vacuum, i.e. in inelastic proton-proton (pp) collisions. Low-mass dielectrons have been measured with ALICE at the LHC in pp collisions at s=7and13TeV, and in Pb–Pb collisions at sNN=2.76TeV. An overview of the results on dielectron production is presented, together with their implications for the direct-photon and heavy-quark production.