  Geospace phenomena such as the aurora, plasma motion, ionospheric currents
and associated magnetic field disturbances are highly organized by Earth's main
magnetic field. This is due to the fact that the charged particles that
comprise space plasma can move almost freely along magnetic field lines, but
not across them. For this reason it is sensible to present such phenomena
relative to Earth's magnetic field. A large variety of magnetic coordinate
systems exist, designed for different purposes and regions, ranging from the
magnetopause to the ionosphere. In this paper we review the most common
magnetic coordinate systems and describe how they are defined, where they are
used, and how to convert between them. The definitions are presented based on
the spherical harmonic expansion coefficients of the International Geomagnetic
Reference Field (IGRF) and, in some of the coordinate systems, the position of
the Sun which we show how to calculate from the time and date. The most
detailed coordinate systems take the full IGRF into account and define magnetic
latitude and longitude such that they are constant along field lines. These
coordinate systems, which are useful at ionospheric altitudes, are
non-orthogonal. We show how to handle vectors and vector calculus in such
coordinates, and discuss how systematic errors may appear if this is not done
correctly.
