Significant are also the extensions of the polaron concept: acoustic polaron, piezoelectric polaron, electronic polaron, bound polaron, trapped polaron, spin polaron, molecular polaron, solvated polarons, polaronic exciton, Jahn-Teller polaron, small polaron, bipolarons and many-polaron systems. These extensions of the concept are invoked, e. g., to study the properties of conjugated polymers, colossal magnetoresistance perovskites,  high- superconductors, layered MgB superconductors, fullerenes, quasi-1D conductors, semiconductor nanostructures.
The possibility that polarons and bipolarons play a role in high- superconductors has renewed interest in the physical properties of many-polaron systems and, in particular, in their optical properties. Theoretical treatments have been extended from one-polaron to many-polaron systems.
A new aspect of the polaron concept has been investigated for semiconductor nanostructures: the exciton-phonon states are not factorizable into an adiabatic product Ansatz, so that a non-adiabatic treatment is needed. The non-adiabaticity of the exciton-phonon systems leads to a strong enhancement of the phonon-assisted transition probabilities (as compared to those treated adiabatically) and to multiphonon optical spectra that are considerably different from the Franck–Condon progression even for small values of the electron-phonon coupling constant as is the case for typical semiconductor nanostructures.
In biophysics Davydov soliton is a propagating along the protein α-helix self-trapped amide I excitation that is a solution of the Davydov Hamiltonian. The mathematical techniques that are used to analyze Davydovs soliton are similar to some that have been developed in polaron theory. In this context the Davydov soliton corresponds to a polaron that is (i) large so the continuum limit approximation in justified, (ii) acoustic because the self-localization arises from interactions with acoustic modes of the lattice, and (iii) weakly coupled' because the anharmonic energy is small compared with the phonon bandwidth.
It has been shown that the system of an impurity in a Bose–Einstein condensate is also a member of the polaron family. This allows the hitherto inaccessible strong coupling regime to be studied, since the interaction strengths can be externally tuned through the use of a Feshbach resonance. This was recently realized experimentally by two research groups.
The existence of the polaron in a Bose–Einstein condensate was demonstrated for both attractive and repulsive interactions, including the strong coupling regime and dynamically observed.