Intersection theory on Grassmannians was given a positive combinatorial interpretation in the '30s (proven in the '70s). I'll explain many independent generalizations of this problem -- equivariant, K-theoretic, quantum, and others -- and solve many of them using "puzzles", which Tao and I introduced, and Zinn-Justin and I have extended in many ways. A unifying theme will be R-matrices arising from minuscule representations. Physical puzzles will be provided to play with.