Independent Components Analysis (ICA) is a blind source separation method that has been developed to extract the underlying source signals from a set of observed signals where they are mixed in unknown proportions. This is made possible by making the assumption that the “pure” sources are by definition totally unrelated (“independent”) with non-gaussian intensity distributions, whereas their mixtures have more gaussian distributions due to the Central Limit Theorem. ICA can thus be used not just to analyse 2D datasets (e.g. IR spectra) but also multiway datasets (e.g. 3D Excitation-Emission fluorescence spectra) after unfolding. Like other methods based on latent variables, a careful investigation has to be carried out to determine which components are significant and which are not. Therefore, it is important to dispose of valid procedures to decide on the optimal number of independent components (ICs) to extract in the final ICA model. The objective of this presentation is to introduce ICA through the study of several real cases, and to show how it performs compared to other more classical multivariate methods such as Principal Components Analysis (PCA). In this way, the relative advantages and disadvantages of ICA will be pointed highlighted.