  In the recent years, non-Gaussianity and statistical isotropy of the Cosmic
Microwave Background (CMB) was investigated with various statistical measures,
first and foremost by means of the measurements of the WMAP satellite. In this
Review, we focus on the analyses that were accomplished with a measure of local
type, the so-called Scaling Index Method (SIM). The SIM is able to detect
structural characteristics of a given data set, and has proven to be highly
valuable in CMB analysis. It was used for comparing the data set with
simulations as well as surrogates, which are full sky maps generated by
randomisation of previously selected features of the original map. During these
investigations, strong evidence for non-Gaussianities as well as asymmetries
and local features could be detected. In combination with the surrogates
approach, the SIM detected the highest significances for non-Gaussianity to
date.
