We investigate structural, electronic, dynamical, and dielectric properties of zircon (ZrSiO4) within density-functional theory. The atomic structure is fully relaxed and the structural parameters are found to differ by less than 1.5% from the experimental data. The associated electronic band structure and density of states are also presented. Using density-functional perturbation theory, we obtain the phonon frequencies at the center of the Brillouin zone, the Born effective charge tensors, and the dielectric permittivity tensors. The calculated phonon frequencies agree with the infrared and Raman experimental values (rms relative deviations of 2.5%) when available, while the silent modes are predicted to range between 119.6 and 943.3 cm(-1). We compute the Born effective charge tensors, that are found to be quite anisotropic. The electronic and static dielectric permittivity are analyzed in detail. Their difference is mostly due to the lowest infrared-active mode, whose eigenvector corresponds to a distortion of the SiO4 tetrahedra with a displacement of Zr and O atoms in opposite directions.