In this talk opening the present workshop, I give an overview of the state of the art of polaron physics, actual challenges and future directions of research, by congregating international renowned experts coming from interdisciplinary fields of physics, representative of the variegated scientific communities working on the polaron physics. The polaron was proposed by Lev Landau in 1933 to describe an electron moving in a dielectric crystal whose atoms displace from equilibrium to screen the electron charge. Large polarons, whose radii are much larger than the lattice constant, are described by a Hamiltonian named after Herbert Fröhlich. Small polarons, whose radii are of the same order of magnitude as or even smaller than the lattice constant, were first studied in the late 1950s by Theodore Holstein, Jiro Yamashita, and Tatumi Kurosawa. Richard Feynman developed a superior description for the Fröhlich polaron, using path integrals, which represented a corner-stone in the theory of polarons. Polarons come in several varieties, including acoustic polarons, piezopolarons, and polarons in organic materials. Both the large- and small-polaron pictures are used for the interpretation of experiments on optical, thermal, and electromagnetic response in crystals. Recently, frontiers of polaron physics have been substantially extended. Specific polaron states arise at a liquid helium surface due to the interaction of electrons with surface vibrations. Rotational degrees of freedom of an impurity interacting with a bosonic field are able to form the rotational polaron, “angulon”. Finally, polaron-like states can even be found in atomic Bose–Einstein condensates of Bose and Fermi atomic gases. It is remarkable how the Fröhlich continuum polaron, one of the simplest examples of a quantum field theoretical problem, has resisted full analytical solution at all coupling since 1950, when its Hamiltonian was first written. Although a mechanism for the optical absorption of Fröhlich polarons was already proposed a long time ago, some subtle characteristics were only clarified very recently by combining numerical diagrammatic Monte Carlo studies and analytic methods. There are still challenging open problems in the polaron theory. Exactly solvable models might give a rather limited description of polarons in real systems. Qualitative inconsistencies can arise when coupling is assumed to be just to one phonon mode, often taken as dispersionless, and ad hoc approximations for Electron-phonon interaction matrix elements are applied. Hence, ab initio calculations of the phonon spectrum, electron-phonon interaction and polaron properties are required in many cases for which the theory and experiment can be compared in detail.