  Berry phases occur when a system adiabatically evolves along a closed curve
in parameter space. This tutorial-like article focuses on Berry phases
accumulated in real space. In particular, we consider the situation where an
electron traverses a smooth magnetic structure, while its magnetic moment
adjusts to the local magnetization direction. Mapping the adiabatic physics to
an effective problem in terms of emergent fields reveals that certain magnetic
textures - skyrmions - are tailormade to study these Berry phase effects.
