Immediately after the Six Day War, the Ministry of Religious Affairs began excavations along the entire length of the Western Wall. They dug using the same mine method as Warren did - under residential areas with ardent Muslims, in an atmosphere of secrecy. The work continued about for 20 years and finally in 1988 the tunnels were opened for public. Of course, there was a littl bit intifada - when the Northern exit from the tunnels was opened, unrest began among the Palestinians, as a result of which more than 60 people were killed.
The picture shows an underground passage going somewhere in the northern (or eastern) direction under the Muslim Quarter.