The 1967 borders are the most recent broadly recognized boundaries. After the Six Days War, Israel gained control of the West Bank, East Jerusalem, the Golan Heights, and Gaza.
As of today, East Jerusalem is a diverse but uneasy mix of Jews and Palestinians. Israel maintains that a unified Jerusalem is its capital, and this is the de facto situation. According to general peace plans, an eventual Palestinian state is meant to have East Jerusalem as its capital, so this is an obvious conflict point.
The West Bank is divided into three areas: A - administered by the Palestinian Authority, B - jointly administered by the PA and Israel, and C - administered by Israel. Israel has been increasingly building more and more settlements within Area C, which are widely recognized as illegal and being incredibly counter-productive towards peace. The Israelis who move there are often extremely nationalistic and often commit violence against the Palestinians. The IDF routinely conducts operations throughout all areas in order to ostensibly maintain security, though they'll always prioritize Israeli lives over Palestinians.
The naive and now utterly hopeless idealistic peace plan is the creation of a Palestinian state consisting of the West Bank and Gaza with a capital in East Jerusalem, with the city being managed by a bi-national coalition of both governments. Israeli settlements within the West Bank would be either abandoned or annexed into Israel with an equal amount of land being swapped from Israel to Palestine. Some kind of stable passage would be created to connect Gaza and the West Bank.
One issue is that a not-small portion of Israelis believe themselves to be entitled to the entire land by virtue of religion, and see continued settlement of the West Bank as furthering this goal. These people suck and aren't that much better than Hamas, though they're not quite as barbaric. The much harder issue is that no Israeli will never allow this solution to happen unless Israel's security is guaranteed, and there is simply zero trust in that, especially now. Israel will not allow itself to sit next to a state run by terrorists that are hell-bent on killing every Jew in the country.
On the matter of international law, Israel justifies its actions by accurately stating that no internationally recognized state lays claim to the West Bank - Jordan withdrew all claims in 1967 - and as such they have a right to settle it. Essentially no other countries have recognized that claim, and there has always been a general agreement that the West Bank will form the basis of a future Palestinian state. Israel certainly hasn't acted in a way that furthers this, but as I said before, its red line is that it will not tolerate security threats to its existence. Militant Palestinian groups attacking Israel only makes peace more and more impossible.
So long as many Palestinians see the mere existence every Jew in Israel as a crime and a target, Israel will see every Palestinian as a potential threat, and the fact of the matter is that Israel holds the guns.
