Magnetic fields in stars, planets, accretion discs, and galaxies are believed to be the result of a dynamo process converting kinetic energy into magnetic energy. This work focuses on the solar dynamo, but dynamos in other astrophysical systems will also be addressed. In particular, direct high-resolution three-dimensional simulations are used to understand particular aspects of the solar dynamo and ultimately to simulate the solar dynamo as a whole. Phenomenological approaches will be avoided in favor of obtaining rigorous results. A major problem is catastrophic quenching, i.e. the decline of dynamo effects in inverse proportion to the magnetic Reynolds number, which is huge. Tremendous advances have been made in the last few years since the cause of catastrophic quenching in dynamos has been understood in terms of magnetic helicity evolution. The numerical tools are now in place to allow for magnetic helicity fluxes via coronal mass ejections, thus alleviating catastrophic quenching. This work employs simulations in spherical shells, augmented by Cartesian simulations in special cases. The roles of the near-surface shear layer, the tachocline, as well as pumping in the bulk of the convection zone are to be clarified. The Pencil Code will be used for most applications. The code is third order in time and sixth order in space and is used for solving the hydromagnetic equations. It is a public domain code developed by roughly 20 scientists world wide and maintained under an a central versioning system at Nordita. Automatic nightly tests of currently 30 applications ensure the integrity of the code. It is used for a wide range of applications and may include the effects of radiation, self-gravity, dust, chemistry, variable ionization, cosmic rays, in addition to those of magnetohydrodynamics. The code with its infrastructure offers a good opportunity for individuals within a broad group of people to develop new tools that may automatically be useful to others.