We dealt with quasimap theory and its applications to mirror symmetry. Especially, we suggested the way how to make conjectural formula explicitly, which is so called ``wall crossing formula", by accounting for the relationship between Gromov-Witten theory and quasimap theory. Also, we explained the relationship between Landau-Ginzburg model and quasimap thoery for known cases. Using this result, we calculated the genus 1 Gromov-Witten invariants for some Calabi-Yau varieties. Finally, we showed that how A-twisted gauged linear sigma model and quasimap theory are related and some correlators defined separately in both theories are matched in some cases. The matched correlators are well-known quatity, so called Yukawa coupling.