First, what is it? Here's a British Library curator, Scot McKendrick, talking about it in July 2007.
Here's another curator of the BL, Juan Garces, describing the codex, its origin and purpose in a talk or podcast given in April 2007.
Most recently, Prof. Nicholas Pickwoad of Camberwell College of Arts describes the joys and challenges of preserving and digitizing Codex Sinaiticus in the Library of the Monastery of St Catherine on Mount Sinai. Scroll down this link. This podcast seems to be from a talk he gave at the BL this month.
The monastery of St.Catherine is a Greek Orthodox monastery at the foot of Mount Sinai where Moses received the Ten Commandments. In 1761 an Italian traveller Donati identified Greek manuscripts he saw there among them Codex Sinaiticus on a visit to the monastery. This report indicates that the monks recognized something of the importance of the manuscript in spite of Constantine von Tischendorf's claims to the contrary. The monks stored manuscript fragments in wicker baskets described by von Tischendorf as "waste paper baskets" to justify his removal of the Codex from the monastery and his failure to return it.