An overview is presented of the theory of continuum (“Fro¨hlich‐Pekar”‐) polarons. Experimental manifestations of polarons are analysed and compared to theory. The emphasis is on the response characteristics of one‐ and many polarons: optical absorption, cyclotron resonance, photoluminescence, Raman scattering. I consider free polarons and polarons confined in space, polarons in 3D, 2D, 0D (quantum dots). © 2003 American Institute of Physics