Cells within developing tissues rely on morphogens to assess positional information. Passive diffusion is the most parsimonious transport model for long-range morphogen gradient formation but does not, on its own, readily explain scaling, robustness and planar transport. Here, we argue that diffusion is sufficient to ensure robust morphogen gradient formation in a variety of tissues if the interactions between morphogens and their extracellular binders are considered. A current challenge is to assess how the affinity for extracellular binders, as well as other biophysical and cell biological parameters, determines gradient dynamics and shape in a diffusion-based transport system. Technological advances in genome editing, tissue engineering, live imaging and in vivo biophysics are now facilitating measurement of these parameters, paving the way for mathematical modelling and a quantitative understanding of morphogen gradient formation and modulation.