The reaction field of a water molecule in liquid water has been computed with the help of continuum, discrete-continuum, and discrete models, using density functional theory calculations. In the continuum model, the liquid is simply described by a polarizable dielectric medium. The solute is placed in a cavity defined by a scaled van der Waals surface. Two different sets of van der Waals radii have been used for the atomic spheres. The discrete-continuum model consists of a quantum molecule surrounded by four classical molecules, the resulting aggregate being embedded in a dielectric continuum. Finally, in the discrete model, a molecular dynamics simulation is carried out for a quantum molecule in a box containing 215 classical molecules with periodic boundary conditions. The reaction field and the induced dipole moment in the standard continuum model are substantially underestimated. However, the use of optimized van der Waals radii for the atomic spheres produces a notable improvement. The discrete-continuum and discrete models lead to close results that are in good agreement with experimental data and previous theoretical estimations. For instance, the induced dipole moment (0.80 and 0.82 D for discrete-continuum and discrete models, respectively) compares well with the experimental estimate (0.75 D) and with Car-Parrinello simulations (1.08 D). The reaction field potential is analyzed in terms of multipole moment contributions. The role of the first shell and bulk solvent are also examined.