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In algebraic geometry and number theory, objects often naturally come equipped with a monodromy or Galois action. Studying this action gives us insight into the structure of the object. Harris initiated the study of the monodromy of enumerative problems, like "how many lines are on a cubic surface?''. A Fano problem is an enumerative problem of counting linear subspaces on complete intersections in projective space, like counting lines on a cubic surface or 2-planes on the intersection of 3 quadrics in $P^8$. In this talk, I discuss the monodromy of Fano problems, and a proof that the monodromy groups of most Fano problems are large. This is joint work with Borys Kadets.