We discuss the formation of graded morphogen profiles in a cell layer by nonlinear transport phenomena, important for patterning developing organisms. We focus on a process termed transcytosis, where morphogen transport results from the binding of ligands to receptors on the cell surface, incorporation into the cell, and subsequent externalization. Starting from a microscopic model, we derive effective transport equations. We show that, in contrast to morphogen transport by extracellular diffusion, transcytosis leads to robust ligand profiles which are insensitive to the rate of ligand production.