In the last 20 years or so, since the publication of a seminal paper by Watts and Strogatz (Nature 393(6684):440–442, 1998), an interest in topological explanations (Huneman in Synthese 177:213–245, 2010) has spread like a wild fire over many areas of science, e.g. ecology, evolutionary biology, medicine, and cognitive neuroscience. The topological approach is still very young by all standards, and even within special sciences it still doesn’t have a single methodological programme that is applicable across all areas of science. That is why this special issue is important as a first systematic philosophical study of topological explanations and their relation to a well understood and widespread explanatory strategy, such as mechanistic one.