In this talk, I will discuss a number of recent works on creating synthetic spaces in ultracold atoms, including topological defects in synthetic high dimensions and synthetic Hall cylinders and torus. The basic ideas include implementing internal states of ultracold atoms as synthetic dimensions and synthesizing them with orbital motions so as to bypass constraints from physical laws. The recent realizations of a synthetic Hall cylinder have opened the door to designing synthetic curved spaces and accessing intriguing quantum phenomena inherent to the topology of spaces. For instance, one could thread a finite effective magnetic flux through the surface of a synthetic torus, an impossible mission in the real space.