Font Size: 

In this talk, we shall review a number of statistical issues that arise in the analysis of Cosmological data. We shall focus in particular on the analysis of Cosmic Microwave Background radiation, a topic which has drawn an enormous amount of theoretical and empirical research over the last two decades; among the issues that arise in this context, we shall review in particular testing for nonGaussianity and isotropy, detection of point sources, power spectrum estimation and the investigation of cross-correlation with other Astrophysical datasets.  As a unifying framework to tackle these issues we shall discuss harmonic analysis for spherical random fields and wavelet/needlet techniques; we shall present some analytical results and discuss a wide range of applications which have been implemented on real data in the last decade.