Space Science Reviews: In this article we review small-scale dynamo processes that are responsible for magnetic field generation on scales comparable to and smaller than the energy carrying scales of turbulence. We provide a review of critical observation of quiet Sun magnetism, which have provided strong support for the operation of a small-scale dynamo in the solar photosphere and convection zone. After a review of basic concepts we focus on numerical studies of kinematic growth and non-linear saturation in idealized setups, with special emphasis on the role of the magnetic Prandtl number for dynamo onset and saturation. Moving towards astrophysical applications we review convective dynamo setups that focus on the deep convection zone and the pho- tospheres of solar-like stars. We review the critical ingredients for stellar convection setups and discuss their application to the Sun and solar-like stars including comparison against available observations.
Comparison of Bz at optical depth unity in two dynamo simulations with different domain sizes. The full horizontal extent shows results from a simulation in a 98.304 × 98.304×18.432 Mm^3 domain. The small red box indicates a simulation in a 24.576×24.576× 7.68 Mm^3. For better visibility we periodically extended this simulation as a 2×2 tile (large red box). The small-scale dynamo simulation in the wider and deeper domain does produce a mixed polarity network structure on scales larger than 10 Mm, which is absent in the smaller domain.