Question: what happened to rory and amy in doctor who

title: The Angels Take Manhattan
text: The Doctor , River , Amy , and Rory suddenly find themselves near the TARDIS in a New York graveyard back in 2012 , Rory 's plan having worked . As the four prepare to depart , Rory catches sight of a tombstone with his name on it . He is then touched by a surviving , albeit weakened , Angel and sent into the past . The Doctor is unable to take the TARDIS back to get him , due to the paradox Rory and Amy created . Amy refuses to be parted from Rory and willingly allows herself to be touched by the same Angel in the hope of being sent back to the same time as he was . Her name then appears along with Rory 's on the tombstone . The Doctor is distraught , but River reminds him that while their fates are now sealed , Amy likely published the Melody Malone book in the past and may have left him a message . The Doctor races back to where they had their picnic and recovers the final page , finding the afterword written by Amy to him . Amy explains that she and Rory lived out a good and happy life for themselves , and asks the Doctor to visit her childhood self to assure her that he will come back for her to take her on amazing journeys . The episode ends with a young Amelia Pond sitting in her back garden , then looking up and smiling as the TARDIS engines are heard . 

Answer: answer: The Doctor, River, Amy and Rory suddenly find themselves in a New York graveyard. As the four prepare to depart, Rory catches sight of a tombstone with his name on it. Amy refuses to be parted from Rory. Her name then appears along with Rory's on the tombstone. The Doctor is distraught, but River reminds him that Amy may have left him a message. The Doctor races back and finds the afterword written by Amy. Amy explains that she and Rory lived out a good and happy life for themselves, and asks the Doctor to visit her childhood self to assure her that he will come back for her to take her on amazing journeys.