The graded distribution of morphogens underlies many of the tissue patterns that form during development. How morphogens disperse from a localized source and how gradients in the target tissue form has been under debate for decades. Recent imaging studies and biophysical measurements have provided evidence for various morphogen transport models ranging from passive mechanisms, such as free or hindered extracellular diffusion, to cell-based dispersal by transcytosis or cytonemes. Here, we analyze these transport models using the morphogens Nodal, fibroblast growth factor and Decapentaplegic as case studies. We propose that most of the available data support the idea that morphogen gradients form by diffusion that is hindered by tortuosity and binding to extracellular molecules.