  Magnetic fields play a fundamental role for interior and atmospheric
properties of M dwarfs and greatly influence terrestrial planets orbiting in
the habitable zones of these low-mass stars. Determination of the strength and
topology of magnetic fields, both on stellar surfaces and throughout the
extended stellar magnetospheres, is a key ingredient for advancing stellar and
planetary science. Here modern methods of magnetic field measurements applied
to M-dwarf stars are reviewed, with an emphasis on direct diagnostics based on
interpretation of the Zeeman effect signatures in high-resolution intensity and
polarisation spectra. Results of the mean field strength measurements derived
from Zeeman broadening analyses as well as information on the global magnetic
geometries inferred by applying tomographic mapping methods to
spectropolarimetric observations are summarised and critically evaluated. The
emerging understanding of the complex, multi-scale nature of M-dwarf magnetic
fields is discussed in the context of theoretical models of hydromagnetic
dynamos and stellar interior structure altered by magnetic fields.
