The notion that carriers doped into insulators get dressed by lattice deformations has been around for a long time [1, 2]. A recent development is that this polaron formation can be studied experimentally using angle-resolved photoemission (ARPES), yielding more direct information on the physics than classical transport and optical speแtroscopic methods. Especially when the carrier density is small but finite, where a controlled theoretical framework is lacking, ARPES has been quite revealing. The case has been made that lightly doped cuprates fall victim to small-polaron formation (strong interacting case) that is vulnerable to self-trapping by impurities [3, 4]; in undoped cuprates, the spectral functions reveal Frank–Condon-type broad humps caused by the coupling to multiple phonons, and only when doping is increased does a well-defined quasi-particle (QP) peak start to emerge [3, 4]. Another recent ARPES revelation is found in the context of highly doped manganites in the colossal magnetoresistance regime. At high temperatures ARPES reveals the Frank–Condon humps signaling small polarons, while upon lowering temperature small pole-strength QP peaks appear in addition, indicating that a coherent Fermi liquid is formed from the microscopic polarons [5].