Two-dimensional materials having apertures in their basal planes are described, where at least a portion of the apertures are occluded with a selectively introduced occluding moiety. Occluding moieties that pass into apertures function to occlude apertures. Composite membranes are described having a porous substrate with a two-dimensional material disposed on the membrane and covering only a portion of the pores, wherein at least a portion of uncovered substrate pores are occluded. Pore occlusion can be achieved by introduction of an occluding particle optionally followed by chemical reaction, deformation or swelling of the particle to facilitate occlusion of pores. Two-dimensional materials covering substrate pores can be size-selected and optionally functionalized providing for selective permeability through composite membranes. Methods for occluding defects and apertures in two-dimensional materials and for selectively occluding pores in composite membranes are provided. Selectively occluded materials and membranes are useful in filtration and other applications.