In this talk, I review my recent research on boundary effects in topological insulators and heterostructured materials. In particular, I explain a concept of the boundary charge which facilitates a description of the quantum Hall effects in arbitrary dimensions. A complimentary approach based on the boundary Green’s functions is introduced to study transport phenomena in systems combining materials with various properties, with examples including topological superconductors, semiconductors, and orbital ferromagnets. Finally, I report about a recent application of similar theoretical methods to a careful explanation of the experimental measurements of the photon-qubit bound state resonances in the framework of the microwave waveguide electrodynamics and superconducting transmon qubits.