Abstract Clustering is a concept used in a huge variety of applications. We review a conceptually very simple algorithm for hierarchical clustering called in the following the mutual information clustering (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects X,Y, and Z is equal to the sum of the MI between X and Y, plus the MI between Z and the combined object (XY). We use MIC both in the Shannon (probabilistic) version of information theory, where the “objects ” are probability distributions represented by random samples, and in the Kolmogorov (algorithmic) version, where the “objects ” are symbol sequences. We apply our method to the construction of phylogenetic trees from mitochondrial DNA sequences and we reconstruct the fetal ECG from the output of independent components analysis (ICA) applied to the ECG of a pregnant woman.