Crystal bases provide powerful combinatorial models for representations of quantum groups, with semistandard Young tableaux being the classical type A example. K-theoretic Schubert calculus gives rise to richer families of tableaux, including set-valued and hook-valued tableaux, whose generating functions are stable Grothendieck polynomials and their canonical analogues. In this talk, I will describe how these K-theoretic tableau models can be understood through crystal-theoretic methods. A key tool for understanding these objects is an "uncrowding" operator, which relates more complicated tableaux back to classical ones while preserving structural features. Building on Buch's uncrowding operator for set-valued tableaux, I will discuss a recent extension to hook-valued tableaux. By studying these operators, we uncover a "hidden" symmetry of hook-valued tableaux through jeu de taquin, using a classical result of Benkart, Sottile, and Stroomer. This talk is based on joint work with Jang, Kim, Pappe, Poh, and Schilling.