  Global dynamo simulations solving the equations of magnetohydrodynamics (MHD)
have been a tool of astrophysicists who try to understand the magnetism of the
Sun for several decades now. During recent years many fundamental issues in
dynamo theory have been studied in detail by means of local numerical
simulations that simplify the problem and allow the study of physical effects
in isolation. Global simulations, however, continue to suffer from the age-old
problem of too low spatial resolution, leading to much lower Reynolds numbers
and scale separation than in the Sun. Reproducing the internal rotation of the
Sun, which plays a crucual role in the dynamo process, has also turned out to
be a very difficult problem. In the present paper the current status of global
dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to
understand how the large-scale magnetic fields, i.e. whose length scale is
greater than the scale of turbulence, are generated in the Sun. Some lessons
from mean-field theory and local simulations are reviewed and their possible
implications to the global models are discussed. Possible remedies to some
current issues of solar simulations are put forward.
