The commissioning of Tevatron collider Run II began in spring of 2001. Although the increase in luminosity was slower than expected, peak luminosities have since reached 4.5e31/cm2/s. In order to further increase the Tevatron luminosity, many issues are being actively addressed. Among them are beam-beam effects, limitations in the pbar production and issues related to the main superconducting magnets. It was found that many dipoles are rolled such as to induce vertical bending of the beam. Recently, a change of the multipolar field content of the main dipole magnets due to coil movements in the iron yoke was discovered, giving rise to a strong coupling between horizontal and vertical betatron motion. The compensation of dynamic effects in the Tevatron was revisited in the light of recent advances in the field leading to the proposal of improvements of the existing chromaticity correction. These and other magnet related issues will be presented in this talk. Lessons that could be learned from the experience with the magnet system in the Tevatron in view of the Cern's LHC will also be discussed.