Abstract: Over the last two decades, Cosmology has experienced a sort of revolution, where a flood of data of unprecedented accuracy has become available by means of a number of different ground-based and satellite experiments. A particularly striking example is given by the analysis of Cosmic Microwave Background radiation (CMB); loosely speaking, CMB can be viewed as a snapshot of the Universe taken at the age of recombination, i.e. "soon after" the Big Bang: very detailed maps have been produced by the NASA satellite WMAP (2003-2009) and by the ESA satellite Planck (2013-2018). The analysis of these maps entails a number of extremely interesting mathematical questions, mostly related to the geometry of spherical random fields. In this talk, we shall be concerned in particular with issues related to detection of point sources (Galaxies) in CMB Data; we shall discuss in particular the connection with spherical wavelets, distribution of critical points for spherical random fields, and multiple testing procedures.