We show that the horofunction compactification of Teichm\"uller space with
the Teichm\"uller metric is homeomorphic to the Gardiner-Masur
compactification.Comment: Final version, the proof of Proposition 5.1 is improved. To appear in
Handbook of Teichm\"uller Theory, Vol. 4, A. Papadopoulos (ed.), EMS
publishing house, Z\"urich 201