In electronics, information is transferred with charge carriers, whose motion can be easily controlled with external fields. This is not the case of phononics, where the manipulation of phonons is intrinsically more challenging: this is why we live in a world of electronic devices and heat is normally regarded as a source of loss.
We are trying to reverse this viewpoint and move to a new paradigm where heat can be actively used to transfer energy, thus information, in a controllable way. The long-standing goal is designing devices acting as logic gates and thermal transistors, which would pave the way to signal processing with phonons.
The intrinsic difficulty in manipulating phonons is often ascribed to the fact that they do not possess a net charge or a mass; thus, it is difficult to control their propagation by means of external fields. However, this is not entirely true. Insulators or semiconductors often feature vibrational modes that involve atoms with different charges, which can be acted upon by an external electric field, resulting in a modulation of the thermal conductivity. This was shown by Torres et al. , who predicted this effect in lead titanate and demonstrated that such electrophononic response can be tuned (and increased by orders of magnitudes!) by means of mechanical deformations of the material.
A related challenge is creating materials by design, with tailor-made thermal properties. A way to achieve this goal is creating superlattices: periodic structures made of an ordered sequence of building blocks or layers of different materials, which behave like metamaterials, with their own properties that can be tuned by controlling the stacking of the building blocks (composition, structure, width…). In a joint theoretical and experimental study, De Luca et al.  demonstrated for the first time the tuning of the vibrational properties of a crystal phase superlattice, a novel type of superlattice whose basic building blocks, rather than made of different materials, are made of different crystal phases of the same material.
Figure: TEM image of the atomic arrangement of a twin superlattice. The change in the stacking of the different layers can be appreciated and is also in the cartoon that displays the atomic arrangement around the twin inversion plane. The right-hand side panel displays the Raman signature of the twin superlattice.