At the insitigation of the American actor Sam Wanamaker the new Globe Theatre was built according to an original Elizabethan plan. The design team comprised Theo Crosby of Pentagram as the architect, Buro Happold as structural and services engineers and Boyden & Co as quantity surveyors. It opened in 1997 under the name "Shakespeare's Globe Theatre" and now stages plays every summer (May to October).
There are now plans to build a Globe Theatre in a fort on Governor's Island in New York. You can see the second part of this video and satellite imagery of the fort here.