Spin foam models are models for space time built from discrete chunks of quantized geometry. In the asymptotic regime the classical geometry is regained.
In the last year we have seen rapid developments in our understanding of this geometry at the level of the entire partition function. In particular it was found that the geometries that contribute to the partition function in the asymptotic regime satisfy accidental curvature constraints.
I will discuss the classic results and role of asymptotics, the recent results and their impact on the interpretation of these models.