The LHC heavy ion physics program aims at investigating the properties of strongly interacting matter at extreme energy density where the formation of the Quark Gluon Plasma (QGP) is expected. Among the most promising observables, dilepton are especially relevant since they carry undistorted information from the earliest and hottest stages of the collision. Moreover, quarkonium states provide, via their leptonic decay, one of the most promising observable for the study of the QGP. ALICE (A Large Ion Collider Experiment) will be the only detector dedicated to the study of nucleus-nucleus collisions at the LHC. (Di-)leptons will be measured in ALICE through the electron channel in the central region as well as through the muon channel in the forward region. After an introduction on the relevance of dilepton production in heavy ion collisions at the LHC and the description of the ALICE detector, the expected performances of the apparatus for dilepton measurements will be reviewed.