After Israel declared its independence in 1948, it was attacked en masse by its Arab neighbors. At the end of that conflict, East Jerusalem fell under the control of Jordanian forces. Christians and Jews were denied access to their holy sites in the old city, including the Church of the Holy Sepulcher and the Western Wall. In violation of UN General Assembly Resolution 181, Arab forces also destroyed many Jewish synagogues, and bulldozed Jewish graves on the Mount of Olives so that a hotel access road could be built.
Jerusalem remained divided until the 1967 Six-Day War, during which Israeli forces recaptured the old city, and unified it. Under Israeli control, Christian, Muslim, and Jewish people administer their respective holy sites within the city, and each is allowed free access to those sites.
For further background: