Schubert calculus has garnered significant attention in recent years due to its importance across various fields, including geometry, topology, combinatorics, and representation theory, particularly in the study of K-theoretic ring structure constants of the affine Grassmannian. Lam et al. introduced a family of symmetric functions to represent the K-theoretic homology of the affine Grassmannian, which we refer to as K-theoretic symmetric functions. Motivated by the analysis of Euler characteristics of vector bundles on the flag variety, Blasiak et al. demonstrated that a specific class of K-theoretic symmetric functions, known as K-k-Schur functions, forms a subset of the combinatorial family of symmetric functions called Catalan functions. This result offers a promising framework for much of the ongoing research on K-theoretic symmetric functions. In this talk, I will present our recent work on K-theoretic symmetric functions, in particular on K-k-Schur functions, in the context of their Catalan forms.