  Cell fate decisions emerge as a consequence of a complex set of gene
regulatory networks. Models of these networks are known to have more parameters
than data can determine. Recent work, inspired by Waddington's metaphor of a
landscape, has instead tried to understand the geometry of gene regulatory
networks. Here, we describe recent results on the appropriate mathematical
framework for constructing these landscapes. This allows the construction of
minimally parameterized models consistent with cell behavior. We review
existing examples where geometrical models have been used to fit experimental
data on cell fate and describe how spatial interactions between cells can be
understood geometrically.
