abstract: Networks of interacting qubits are a generalization of spin chains. These are of theoretical importance for the study of many-body quantum systems and could constitute a good test ground for technologies spanning from quantum key distribution in multi-user networks to various nano-scale devices. Networks of interacting qubits are also considered to be good candidates for engineering good quantum channels and allow information transfer between distant particles therefore covering the role of quantum buses. I shall review the mathematical perspective on these topics, with particular attention to design of networks for perfect state transfer. The technical tools include algebraic and spectral graph theory, combinatorial number theory, etc.