The observational evidence that dark matter comprises most of the mass in the Universe is strong, but its nature remains a mystery. In this thesis two different approaches have been followed to characterise the dark matter:

i) Using X-ray observations of dark matter dense regions in various astrophysical objects, the dark matter emission has been constrained in general. For specific candidates such as sterile neutrinos and axions the emission constraints have been converted to constraints in the characterising
parameter space.

ii) The validity of basic assumptions made when deriving the mass of galaxy clusters from X-ray observations have been tested. In the specific case of Abell 1689, high quality data allowed for the identification and exclusion of substructure improving the agreement between the mass profiles obtained from X-ray and gravitational lensing analyses.