Rapid miniaturization of electronic devices to nanoscale range requires new approaches for efficient management of their heat and electrical conductions. One of these approaches, referred to as phonon engineering, is related to optimization of thermal and electronic properties of nanostructures due to modification of their phonon properties [1-2]. Graphene and graphene-based nanostructures are prospective materials for future micro- and nanoelectronics owing to their unusual thermal and electrical properties [3-5].  In this talk I review recent theoretical and experimental results on phonon modes and specific heat of single-layer graphene (SLG), bilayer graphene (BLG) and twisted bilayer graphene (T-BLG) [6]. It has been demonstrated that contrary to a conventional believe the dispersion of the out-of-plane acoustic phonons – referred to as ZA phonons – deviates strongly from a parabolic law starting from the frequencies as low as ~100 cm-1. The latter leads to the breakdown of the linear dependence of the specific heat on temperature T: in SLG ~T only for T<15 K, while specific heat of BLG and T-BLG demonstrates Tn dependence with n>1 even at small temperatures ~ 1 K [7].