The field of astrophysics and cosmology of galaxy clusters is so broad that such a review has to concentrate on some key topics. I have chosen to concentrate on fields where I have seen some important recent progress. Therefore I hope to provide an overview on our understanding of the statistical distribution of galaxy cluster structure and scaling relations, comparison of the X-ray and optical appearance of galaxy clusters, the calibration of galaxy cluster mass weighing, and the study of the stellar and gas mass fractions and the thermodynamic state of the intracluster medium have. Further interesting topics concern information we obtain from X-ray spectroscopy as the heavy element enrichment of the intracluster medium and in the future information on the amount of turbulence in this plasma. The successful surveys detecting galaxy clusters in the Sunyaev-Zeldovich effect provide a new window for cluster studies to our Universe. An increasing amount of new distant clusters being discovered at several wavelengths provide a larger leverage to study galaxy cluster evolution.

Almost all of this new observational information also helps to improve our cosmological studies with galaxy clusters. Thus the recent progress in cluster cosmology is marked to a large degree by improving the systematics of the studies. Promising new galaxy cluster surveys at different wavelengths are at the horizon, hopefully providing us with the means to perform the next step of precision cosmological studies.