During embryonic development, diffusible signaling molecules called morphogens are thought to determine cell fates in a concentration-dependent manner, and protocols for directed stem cell differentiation are based on this picture. However, in the mammalian embryo, morphogen concentrations change rapidly compared to the time for making cell fate decisions. It is unknown how cells process these changing signals, and whether the precise time course of ligand exposure plays a role in cell fate determination. Human embryonic stem cells (hESCs) can form self-organized patterns that mimic the embryo, but provide experimental control unachievable in living embryos, making them ideally suited to quantitatively explore underlying mechanisms. In this talk I will discuss my recent work addressing the role of ligand dynamics in differentiation and patterning of hESCs, focusing on two morphogens that are crucial for vertebrate gastrulation: Nodal and BMP4. My results break with the paradigm of concentration-dependent differentiation and demonstrate an important role for morphogen dynamics in the cell fate decisions associated with mammalian gastrulation. They suggest a highly dynamic picture of embryonic patterning where some cell fates depend on rapid concentration increase rather than absolute levels, and point to ligand dynamics as a new dimension to optimize protocols for directed stem cell differentiation.