It started as a round tower in the early 15th century and was then continuously expanded through the 16th, 17th and 19th centuries. It was linked with a chain to the Round Tower on Portsmouth side that could be raised from the sea bed to the surface to protect the harbour. It is still MOD property. As far as I know, it is the oldest fortified position in Britain still occupied by the armed forces.
The tower in the background is the 100 Foot high water tank - submarine escape training tower. All RN submariners are required to simulate an escape from the bottom of the tower and float up to the top.