Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo.We review the current status of dynamo theory and discuss various numerical simulations designed either to explain particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows: Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem. Large-scale galactic magnetic fields of microgauss strengths can probably be explained only if helical magnetic fields of small or moderate length scales can be rapidly ejected or destroyed. Small-scale dynamos are important throughout a galaxy's life and probably provide strong seed fields at early stages. The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work.