Homological stability for spaces of embedded subsurfaces of an at least 6 dimensional simply-connected manifold has been proven in 2017 by Frederico Cantero and Oscar Randal-Williams. In this talk I will explain parts of their proof and explain how to extend this to subsurfaces, which can carry a large class of tangential structure. In particular I will explain how to prove homological stability for spaces of symplectic subsurfaces.