In this Perspective, I present a concise account concerning the emergence of the research field investigating the phononic and thermal properties of graphene and related materials, covering the refinement of our understanding of phonon transport in two-dimensional material systems. The initial interest in graphene originated from its unique linear energy dispersion for electrons, revealed in exceptionally high electron mobility, and other exotic electronic and optical properties. Electrons are not the only elemental excitations influenced by a reduction in dimensionality. Phonons-quanta of crystal lattice vibrations-also demonstrate an extreme sensitivity to the number of atomic planes in the few-layer graphene, resulting in unusual heat conduction properties. I outline recent theoretical and experimental developments in the field and discuss how the prospects for the mainstream electronic application of graphene, enabled by its high electron mobility, gradually gave way to emerging real-life products based on few-layer graphene, which utilize its unique heat conduction rather than its electrical conduction properties.