The cloisters at Chester Cathedral were largely rebuilt around 1525-30, during the final days of the abbey, with rib-vaults and perpendicular windows.
Shown here is the North Cloister which adjoins the Refectory. The long stone shelf seen on the left of the photograph was the lavatorium, where bowls were set out to enable the monks to wash before meals.
After the Dissolution, the cloisters lost their religious function and fell into disrepair- the south one was actually demolished- until an extensive programme of restoration was carried out in 1911-13 by Sir Giles Gilbert Scott, architect of the great Liverpool Cathedral. His grandfather, Sir George Gilbert Scott had previously extensively restored- and, more controversially, 'improved'- much of the rest of the Cathedral in 1868-76.

To read much more about the history of this great building, including a curious legend regarding a Devil's hoofprint here in the cloisters, visit the Cathedral chapters of Chester: A Virtual Stroll Around the Walls