Measurements of charmless semileptonic B-meson decays and the CKM matrix element |Vub| are reported based on a sample of 88 million [Formula: see text] events recorded with the BABAR detector. Decays B → Xuℓν are selected from both tagged and untagged [Formula: see text] events and separated from the dominant charm background, B → Xcℓν, using different kinematic variables: the lepton momentum Eℓ, the squared four-momentum transfer q2, and the hadronic mass mX. The extrapolation to the total decay rate to determine |Vub| is performed for different theoretical models. We have also measured branching ratios for the exclusive semileptonic decays B → π(ρ,ω,η,η′,a0)ℓν, where a high signal purity is reached by fully or partially reconstructing the second B meson.