  This survey is devoted to recent developments in the statistical analysis of
spherical data, with a view to applications in Cosmology. We will start from a
brief discussion of Cosmological questions and motivations, arguing that most
Cosmological observables are spherical random fields. Then, we will introduce
some mathematical background on spherical random fields, including spectral
representations and the construction of needlet and wavelet frames. We will
then focus on some specific issues, including tools and algorithms for map
reconstruction (\textit{i.e.}, separating the different physical components
which contribute to the observed field), geometric tools for testing the
assumptions of Gaussianity and isotropy, and multiple testing methods to detect
contamination in the field due to point sources. Although these tools are
introduced in the Cosmological context, they can be applied to other situations
dealing with spherical data. Finally, we will discuss more recent and
challenging issues such as the analysis of polarization data, which can be
viewed as realizations of random fields taking values in spin fiber bundles.
