Summary: The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten theory. This note is a survey article on the moduli of stable quasimaps, based on papers by I. Ciocan-Fontanine and B. Kim [Adv. Math. 225, No. 6, 3022–3051 (2010; Zbl 1203.14014)], [I. Ciocan-Fontanine et al., J. Geom. Phys. 75, 17–47 (2014; Zbl 1282.14022)], the author [Stable quasimaps to holomorphic symplectic quotients, arXiv:1005.4125] as well as the author’s talk at Kinosaki Algebraic Geometry Symposium 2010.