We seek to obtain a picture of the interstellar magnetic field in the Galactic center region that is as clear and complete as possible. We review the observational knowledge that has built up over the past 25 years on interstellar magnetic fields within 200 pc of the Galactic center. We then critically discuss the various theoretical interpretations and scenarios proposed to explain the existing observations. We also study the possible connections with the general Galactic magnetic field and describe the observational situation in external galaxies. We propose a coherent picture of the magnetic field near the Galactic center, which reconciles some of the seemingly divergent views and which best accounts for the vast body of observations. Our main conclusions are the following. In the diffuse intercloud medium, the large-scale magnetic field is approximately poloidal and its value is generally close to equipartition with cosmic rays ( 10 mu G), except in localized filaments where the field strength can reach 1 mG. In dense interstellar clouds, the magnetic field is approximately horizontal and its value is typically 1 mG.