  We review two powerful methods to test the Gaussianity of the cosmic
microwave background (CMB): one based on the distribution of spherical wavelet
coefficients and the other on smooth tests of goodness-of-fit. The spherical
wavelet families proposed to analyse the CMB are the Haar and the Mexican Hat
ones. The latter is preferred for detecting non-Gaussian homogeneous and
isotropic primordial models containing some amount of skewness or kurtosis.
Smooth tests of goodness-of-fit have recently been introduced in the field
showing some interesting properties. We will discuss the smooth tests of
goodness-of-fit developed by Rayner and Best for the univariate as well as for
the multivariate analysis.
