We present an overview of "XSAPT", a family of quantum chemistry methods for noncovalent interactions. These methods combine an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large noncovalent assemblies such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and two new approaches are introduced here in an attempt to improve this situation: (1) third-generation empirical atom-atom dispersion potentials, and (2) an empirically scaled version of second-order SAPT dispersion. Comparison to high-level ab initio benchmarks for dimers, water clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as O(N(3))-O(N(5)) with respect to monomer size, N, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of XSAPT calculations makes them trivially parallelizable, such that wall times scale linearly with respect to the number of monomer units. XSAPT-based methods thus open the door to both qualitative and quantitative studies of noncovalent interactions in clusters, biomolecules, and condensed-phase systems.