Two-dimensional polymers (2DPs) are a class of two-dimensional (2D) materials that combine atomic thinness and molecular functionality. Like all 2D materials, 2DPs have an anisotropic structure where molecular moieties are connected by chemical bonds in-plane but loosely bounded out-of-plane through van der Waals (vdW) forces, allowing 2DPs to be isolated as ultrathin monolayers. What distinguishes 2DPs from their inorganic counterparts are the molecular lattice constituents, which give rise to almost infinite varieties of 2DPs. Particularly, molecular lattice constituents often lead to an intrinsic porosity in 2DPs, making them ideal candidates for membrane-related applications. In this dissertation, we will investigate the large-scale synthesis of 2DPs and explore their application as a membrane for osmotic power generation. First, we will introduce an interfacial synthesis method for monolayer 2DPs up to inch-scale. This method is compatible with various 2DPs structures and chemistries. We will use this method to generate homogeneous monolayer 2DPs and investigate their structural and chemical properties. Using this approach, we will also demonstrate the capability of generating hybrid vdW heterostructures, from which large-scale electrical device arrays can be fabricated. Second, we will use our ultrathin nanoporous 2DPs as a permselective membrane for osmotic power generation. The chemical and structural versatility of 2DPs allow for a rational bottom-up design of a covalently linked 2DP membrane with proper pore size and functionalization that fall in the “Goldilocks” zone for osmotic power generation. The mechanics of short-range interaction-based permselectivity in our membrane is investigated using molecular dynamics simulations, and the unique mechanism is leveraged for ion-specific transport and gateable osmotic power generation. In the end, we propose several new directions for further improving the synthesis of 2DPs and expanding their applications.