[en] ALICE (A Large Ion Collider Experiment) is designed to study the strongly-interacting medium created in heavy-ion collisions at LHC energies, the Quark-Gluon Plasma (QGP). Charm and beauty quarks are powerful probes to study the QGP in heavy-ion collisions: produced in hard partonic scattering processes on a short time scale, they are expected to traverse the QCD medium, interacting with its constituents and losing energy through radiative and collisional processes. In ALICE, open-charm production is studied through the reconstruction of the hadronic decays of D"0, D"+, D"*"+ and D_s"+ mesons at mid-rapidity. The high precision tracking, good vertexing capabilities and excellent particle identification offered by ALICE allow for the measurement of particles containing heavy quarks (particularly D mesons) in a wide transverse-momentum range in pp, p-Pb and Pb-Pb collisions. A review of the main results on D-meson production in pp collisions at = 7 TeV, Pb-Pb collisions at = 2.76 TeV and the most recent results in p-Pb collisions at = 5.02 TeV will be presented. In particular, the p_T-differential yields and cross sections in the three collision systems, the nuclear modification factors R_A_A and R_p_P_b in Pb-Pb and p-Pb collisions, and the elliptic flow in Pb-Pb collisions will be discussed. The D-meson yield in pp and p-Pb collisions will also be shown as a function of charged-particle multiplicity. (paper)