The BBC's Middle East editor Jeremy Bowen examines key questions arising from Israeli Prime Minister Ariel Sharon's departure from the Likud party.
Will it be good for the peace process?
The first thing is that there is no peace process between Israel and the Palestinians.
The Oslo process that began with secret negotiations in Norway set sail with handshakes and hope from the lawn of the White House in 1993. It dwindled and died through the rest of the 1990s and was finally swept away in 2000 by the Palestinian uprising and Israel's fierce military response.
Recent attempts at peace in the region have ended in stalemate
There are contacts between the two sides, most promisingly in the last few weeks with the help of US Secretary of State Condoleezza Rice to reopen the borders of Gaza.
There was a certain amount of co-ordination when Ariel Sharon unilaterally pulled Israelis out of Gaza in the summer.
But in the words of one of Ms Rice's most senior officials, most of the work has been at colonel level and below. That does not amount to a peace process.
We will know it when it starts again. It will require a sustained diplomatic push by the Americans and proper contacts between Israelis and Palestinians, including presidents and prime ministers.
Will Israeli Prime Minister Ariel Sharon take more unilateral action, like the pullout from Gaza?
Ariel Sharon said when he was leaving Likud that he planned no more unilateral actions.
Instead he was going to rely on the "road map". That is a phased programme of actions and negotiation that, if followed, is supposed to lead all parties to peace and the establishment of a Palestinian state alongside Israel.
Israeli leader Ariel Sharon says he will stick to the roadmap
The problem is that it is stuck in its first phase, which is supposed, among other things, to end terror and freeze the construction of Jewish settlements.
Neither side is keeping its promises to take action. And it has been on the table for two-and-a-half years.
The chances are that everything will stay on hold until after Palestinian parliamentary elections in January and the Israeli general election, which looks as if it will be in March.
What if Sharon wins the elections?
If Mr Sharon's new party gets enough seats to form a coalition for him to lead, things may start moving.
Saeb Erekat, the veteran Palestinian negotiator, certainly hopes so. After Mr Sharon's announcement that he was leaving Likud he described the change that was happening in Israeli politics as "volcanic".
He says he will work through the "road map".
But if the Palestinian leader, Mahmoud Abbas, does not crack down on armed Palestinian groups like Hamas to Israel's satisfaction - and he probably will not - then Mr Sharon might not feel it necessary to fulfil his obligations.
Many doubt whether Palestinian militants will bow to Mr Abbas
Mr Sharon has not said much in public about his plans, except to say that he wants to fix a final and permanent border between Israel and the Palestinians.
He wants the border to bring in all the big Israeli settlements that have been built on land Israel captured in the 1967 Middle East war.
Smaller, isolated settlements, so far unnamed, will be removed. Mr Sharon also wants Israel to control parts of the West Bank that he believes are strategically vital.
He insists he will achieve it all through the internationally sanctioned road map.
But if he decides the "road map" is not working, and if US President George W Bush decides it is not Israel's fault, then stand by for more unilateral action by Mr Sharon.