Single and multilayer graphenes are among the most promising systems for the development of carbon-based devices in electronics. The detection and analysis of the spectral properties of optical phonons in single- and multi-layer graphene provides a powerful tool not only for investigating the role of the underlying electron-phonon interaction, but also for a careful characterization of the systems. While large amount of work along this direction has initially focused on Raman spectroscopy, phonon anomalies have been recently detected also in the infrared optical conductivity of bilayer graphene, revealing a remarkable tunable dependence of the intensity and of the Fano lineshape asymmetry on the external gate voltage. In this talk I will present a simple theoretical framework which permits to understand at the same time the phonon intensity and the Fano lineshape asymmetry. A complete phase diagram of the optical phonon response is also presented, as a function of both the charge density and the bandgap, showing a switching mechanism, between the dominance of the Eu and Eg mode. controlled by the external gate voltage. The case of multilayer graphene and graphite is also discussed.