Basic features of large-scale magnetic fields in nearby disk galaxies can be reproduced by Galactic dynamo theory. We use analytical equations of turbulent and mean-field dynamos to explore the generation and evolution of regular magnetic fields in disk galaxies at high-$z$ in the context of a hierarchical dark matter cosmology. Present high-resolution numerical simulations of disk models suggest that a rotating disk can be formed at $z>5$. We demonstrate that early regular fields are already in place at $z \sim
4$ (approximately 1.5 Gyr after the disk formation) in massive gas-reach galaxies ($>10^9$ M$_{\sun}$) which then evolve to
Milky-Way type galaxies. Major and minor mergers influence the star formation rate and geometry of the disk which has the effect of
shifting the generation of regular fields in disks to later epochs. Perspectives to detect the polarized radio emission from disk galaxies with future radio telescopes such as LOFAR and the SKA are also discussed.