  It has been common wisdom among mathematicians that Extended Topological
Field Theory in dimensions higher than two is naturally formulated in terms of
n-categories with n> 1. Recently the physical meaning of these higher
categorical structures has been recognized and concrete examples of Extended
TFTs have been constructed. Some of these examples, like the Rozansky-Witten
model, are of geometric nature, while others are related to representation
theory. I outline two application of higher-dimensional TFTs. One is related to
the problem of classifying monoidal deformations of the derived category of
coherent sheaves, and the other one is geometric Langlands duality.
