About 6 million Israeli citizens and residents over the age of 17 are eligible to cast their votes. The most controversial areas are the Golan Heights and East Jerusalem.
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The elections will see officials elected to some 251 city, town and regional councils across Israel — including in Tel Aviv, Jerusalem and Haifa.
Turnout by the 6 million eligible voters will be a key indicator for next year's general elections.
There are 10,000 polling stations, which are set to stay open until late on Tuesday, and the counting of votes will start immediately afterwards.
Minority, Arab-speaking residents of the Druze community are voting in four villages in the Golan Heights — Majdal Shams, Ein Qinya, Bukata and Masadeh — for the first time since Israel captured the region from Syria during the Six-Day War of 1967.
Druze community elders have threatened to make outcasts of anyone taking part in the elections.
"Candidates and those who come to vote will have a religious and social prohibition put upon them," said Sheikh Khamis Khanjar. "What bigger punishment is there than this?"
"When you are in a state that is giving you all your rights, why wouldn't you vote," said Sahar Said Ahmed, referring to the Druze living in Golan, who enjoy greater economic prosperity than their brethren living in war-scarred Syria.
About 22,000 Druze live on the Golan and consider themselves Syrian, despite living under Israeli rule for more than 50 years. Israel has offered citizenship, but most Druze have rejected it.
The international community has never recognized Israeli sovereignty of the Golan Heights.
East Jerusalem
Palestinian residents of East Jerusalem who have not taken Israeli citizenship are eligible to vote in the local elections.
But most of the 300,000 Palestinians have boycotted the process for decades, refusing to recognize Israel's control of East Jerusalem.
Israel captured the predominantly Arab eastern part of the holy city during the Six-Day War of 1967.
Jerusalem's status remains one of the core issues of the decadeslong Israeli-Palestinian conflict.
Israel sees the entire city as the ancient capital of the Jewish people. The Palestinians also lay claim to the holy city and have repeatedly insisted during peace negotiations that the eastern part of the city be the capital of their future state.
The front-runners in the Jerusalem mayoral race are:
Zeev Elkin, Israel's minister for Jerusalem affairs, who has received the backing of Israeli Prime Minister Benjamin Netanyahu
city council member Moshe Lion, backed by ultra-Orthodox voters
secular candidate and city council member Ofer Berkovitch.
The ultra-Orthodox make up some 10 percent of Israel's population and wield particular influence in Jerusalem. The conservative city has previously had an ultra-Orthodox mayor.
There are four candidates vying to take over from the current mayor of Jerusalem, Nir Barkat, who is leaving office after two five-year terms to pursue national office as part of Netanyahu's Likud party.
Twenty-one percent of Jerusalem's Jews are secular, like former Deputy Mayor Berkovitch and Barkat.
Palestinians, who make up a third of Jerusalem's population, are mostly boycotting the election.
If no candidate receives at least 40 percent of the vote, a runoff will be held on November 13.
City of strife: Jerusalem's complex history
Jerusalem is one of the oldest and most contested cities in the world. Jerusalem is revered as a sacred city by Jews, Muslims and Christians alike. For this reason, there has been controversy over the city to this day.
Image: picture-alliance/Zumapress/S. Qaq
Jerusalem, the city of David
According to the Old Testament, David, king of the two partial kingdoms of Judah and Israel, won Jerusalem from the Jebusites around 1000 BC. He moved his seat of government to Jerusalem, making it the capital and religious center of his kingdom. The Bible says David's son Solomon built the first temple for Yahweh, the God of Israel. Jerusalem became the center of Judaism.
Image: Imago/Leemage
Under Persian rule
The Neo-Babylonian King Nebuchadnezzar II (3rd from the left) conquered Jerusalem in 597 and again in 586 BC, as the Bible says. He took King Jehoiakim (5th from the right) and the Jewish upper class into captivity, sent them to Babylon and destroyed the temple. After Persian king Cyrus the Great seized Babylon, he allowed the exiled Jews to return home to Jerusalem and to rebuild their temple.
The Roman Empire ruled Jerusalem from the year 63 AD. Resistance movements rapidly formed among the population, so that in 66 AD, the First Jewish–Roman War broke out. The war ended 4 years later, with a Roman victory and another destruction of the temple in Jerusalem. The Romans and Byzantines ruled Palestine for approximately 600 years.
Image: Historical Picture Archive/COR
Conquest by the Arabs
Over the course of the Islamic conquest of Greater Syria, Muslim armies also reached Palestine. By order of the Caliph Umar (in the picture), Jerusalem was besieged and captured in the year 637 AD. In the following era of Muslim rule, various, mutually hostile and religiously divided rulers presided over the city. Jerusalem was often besieged and changed hands several times.
Image: Selva/Leemage
The Crusades
From 1070 AD onward, the Muslim Seljuk rulers increasingly threatened the Christian world. Pope Urban II called for the First Crusade, which took Jerusalem in 1099 AD. Over a period of 200 years a total of nine crusades set out to conquer the city as it changed hands between Muslim and Christian rule. In 1244 AD the crusaders finally lost control of the city and it once again became Muslim.
Image: picture-alliance/akg-images
The Ottomans and the British
After the conquest of Egypt and Arabia by the Ottomans, Jerusalem became the seat of an Ottoman administrative district in 1535 AD. In its first decades of Ottoman rule, the city saw a clear revival. With a British victory over Ottoman troops in 1917 AD, Palestine fell under British rule. Jerusalem went to the British without a fight.
Image: Gemeinfrei
The divided city
After World War II, the British gave up their Palestinian Mandate. The UN voted for a division of the country in order to create a home for the survivors of the Holocaust. Some Arab states then went to war against Israel and conquered part of Jerusalem. Until 1967, the city was divided into an Israeli west and a Jordanian east.
Image: Gemeinfrei
East Jerusalem goes back to Israel
In 1967, Israel waged the Six-Day War against Egypt, Jordan and Syria. Israel took control of the Sinai, the Gaza Strip, the West Bank, the Golan Heights and East Jerusalem. Israeli paratroopers gained access to the Old City and stood at the Wailing Wall for the first time since 1949. East Jerusalem is not officially annexed, but rather integrated into the administration.
Israel has not denied Muslims access to its holy places. The Temple Mount is under an autonomous Muslim administration; Muslims can enter, visit the Dome of the Rock and the adjacent Al-Aqsa mosque and pray there.
Image: Getty Images/AFP/A. Gharabli
Unresolved status
Jerusalem remains to this day an obstacle to peace between Israel and Palestine. In 1980, Israel declared the whole city its "eternal and indivisible capital." After Jordan gave up its claim to the West Bank and East Jerusalem in 1988, the state of Palestine was proclaimed. Palestine also declares, in theory, Jerusalem as its capital.