Subjected to some damage over the years by war, pollution and transportation they have long been the subject of heated debate as to whether they should be returned to Greece, and a New Acropolis Museum has even been built in Athens which could house them. Surveys also show that a significant proportion of the great British public want to see them returned.
However, the British Museum, which owes a great deal of its treasures to the plundering days of empire, is legally banned by charter from returning any part of its collection. So, at present they still remain in the British Museum, and look like they will for a while.
If you want to know more, visit http://en.wikipedia.org/wiki/Elgin_Marbles