The quantum cohomology of Grassmannians and other algebraic varieties has been extensively studied because of the surprising utility of ideas from string theory applied to algebraic geometry. The structure constants of the quantum cohomology ring of the Grassmannian, for instance, are morally enumerative invariants "counting" the number of curves passing through particular Schubert varieties in the Grassmannian. Quantum K-theory is a natural extension of quantum cohomology for which the enumerative meaning is much less clear. This talk will introduce quantum K-theory for Grassmannians and give a brief (biased) survey of what is known (J-functions, quantum products) and some unsolved questions, with attention to both combinatorics and Schubert calculus.