By work of McQuillan and Brunella, it is known that foliated surfaces of general type with only canonical foliation singularities admit a unique canonical model. It is then natural to investigate the moduli space parametrizing canonical models. One issue is that the condition being a canonical model is neither open nor closed.  In this talk, I will introduce the generalized canonical models to fix this issue and study some properties (boundedness/separatedness/properness/local-closedness) of the moduli space of generalized canonical models.