In this talk I use the idea of branched transport to motivate the study of certain network-like sets with Hausdorff dimension less or equal to one. In the branched transport problem we consider a concave (and thus subadditive) transportation cost which describes the cost of moving mass per unit distance. The branched transport problem seeks for an optimal mass flux between two given probability measures (i.e. source and sink distributions). We proved that it can be written as a shape optimization problem on networks equipped with a network transport cost. In this generalization of the urban planning problem, i.a., the Wasserstein distance between the given probability measures has to be determined. In our case, it corresponds to the problem of finding an optimal transport plan concerning a pseudometric which encodes the cost for traveling from one point to another. This is a joint work with Benedikt Wirth and Bernhard Schmitzer.