A Littlewood-Richardson rule is a positive rule for computing the structure constants of the cohomology ring of flag varieties with respect to their Schubert basis. In recent years new geometric Littlewood-Richardson rules have led to the solution of many important problems, including Klyachko, Knutson and Tao's solution of Horn's conjecture and Vakil's solution of the reality of Schubert calculus. In
this talk I will survey some of the basic geometric ideas that underlie geometric Littlewood-Richardson rules.