The underlying geometry of a gauged linear sigma model (GLSM) consists of a geometric invariant theory (GIT) quotient of a complex vector space by a reductive group G (the gauge group) and a G-invariant polynomial function (the superpotential) on the vector space. GLSM invariants can be viewed as virtual counts of curves in the critical locus of the superpotential, and are mathematically defined by integrating against virtual classes on moduli spaces of Landau--Ginzburg (LG) quasimaps. In this talk, we introduce moduli of prestable LG quasimaps and describe their perfect obstruction theories, based on foundational work of Fan--Jarvis--Ruan and Favero--Kim.