Selected areas of the broad subject of polarons are reviewed here. A derivation of the Fröhlich continuum polaron Hamiltonian is presented in a fairly complete form. Early notable works on the ground state energy and the effective mass of the polaron, as functions of the electron-phonon coupling constant, are also given due attention. Thus the weak and intermediate coupling (Fröhlich, Pelzer and Zienau ; Lee, Low and Pines ; Gurari ), the strong coupling (Landau and Pekar [3,4]) and the all coupling (Feynman ) approaches are discussed in sufficient detail. Later developments, extensive and significant, broadly classified as theoretical developments (such as energy dispersion for large electron momentum, internal excited states and optical absorption phenomenon, alternative and sometimes improved weak-, intermediate- and strong-coupling solutions, etc.) and experimental developments (such as magneto-optical experiments) are also discussed. Only some of the representative magneto-optical experiments are highlighted. Besides these free optical polaron phenomena the important developments in the related areas of the bound polaron (an electron tied to a defect and interacting with the longitudinal optical phonons), the acoustic polaron (an electron interacting with the short-range deformation potential) and the piezo polaron (an electron in a piezoelectric crystal) are also discussed together with some relevant experiments. Instabilities in the electronic states for the free and the bound polarons, obtained in some theoretical model calculations, are treated briefly in the light of current critical appraisals of this phenomenon.