I will discuss the functoriality problem of Gromov-Witten theory, including the past works on crepant transformation conjecture for ordinary flops. The tools used include standard techniques like localization, as well as novel ones (in GWT) like algebraic cobordism. If time allows, I will mention possible functoriality under extremal transitions. This is a joint project with H.-W. Lin and C.-L. Wang and F. Qu.