Unparticle physics is the physics of a hidden sector which is conformal in the infrared and coupled to the Standard Model. The concept of unparticle physics was introduced by Howard Georgi in 2007 and has since then received a lot of attention, including many studies of its phenomenology in different situations. After a review of the necessary background material, the implications of the self-interactions of the unparticle sector for LHC physics is studied. More specifically, analyses of four-body final states consisting of photons and leptons are performed. The results are upper bounds on the total cross sections as well as distributions of transverse momentum.