Schubert Calculus answers basic enumerative questions such as how many lines in the projective space meet four given lines in generic position. Various techniques, from Algebraic Geometry, Algebraic Combinatorics or, sometimes, Representation Theoery, can be used to anser these questions.

In this talk I will study the cohomology of the Grassmannian, from the combinatorial and geometric point of view. My goal is to give a geometric interpretation for Knutson and Tao's "puzzles" (combinatorial objects describing a Littlewood-Richardson (LR) rule for the Grassmannian) via Vakil's recent "geometric LR rule" using degenerations.