Between 1948 and 1967, the area commonly known as the West Bank was controlled by Jordan. The Armistice line of 1949 at the end of Israel's War of Independence was intended by both sides to be temporary and not to constitute a border. From the Arab perspective, recognising a border would Israel. The Jewish residents were expelled by Jordan, while the Arabs were given full Jordanian citizenship rights. The territory has been disputed ever since.
The Oslo Accords (1993-95) divided the West Bank into three areas: A, B and C.
Area A - This is under complete control of the Palestinian Authority and comprises Bethlehem, Nablus, Jenin, Jericho, Ramallah, Qalkilya, Tulkarm and almost all of Hebron. It is illegal for any Israeli to enter
any of these areas.
Area B - This is under civil control of the Palestinian Authority and joint security control between Israel and the Palestinian Authority. This area is largely rural and comprises hundreds of Arab villages. No Israeli is allowed to live anywhere in this area.
Area C - This area is administered by Israel. Fewer than 10% of West Bank Palestinians live in this area, along with 400,000 Israelis. Every Israeli West Bank settlement is in Area C, and Israeli building in Area C is permitted by the Oslo Accords.
If you support a two-state solution, settlements are only a problem in principle if you think that Jews should not be allowed to live in Palestine. Otherwise, it would be entirely possible for the settlements to be absorbed into Palestine in the same way as 1.8 million Arabs live peacefully as full citizens of Israel.
Unfortunately, the Palestinian Authority does indeed believe that Jews should not be allowed to live in Palestine. Indeed, it is illegal under PA law for any Arab to sell land to a Jew anywhere in the West Bank with a potential death sentence for offenders, although since 2006 the PA has preferred to use hard labour as an alternative.
Although the West Bank is often described as 'occupied territory', this is far from clear in law, for several reasons:
(i) No other sovereign state makes any claim on the territory
(ii) If Israel must return the territory because it was acquired by force, to whom should it be returned? Since it was acquired by Jordan by force, and Jordan's occupation was not accepted by the international community, that must also be ruled illegitimate. Before then, it was controlled, but not owned, by the British Empire under the Mandate. Prior to that, it was under the control of the Ottoman Empire, which no longer exists. The last sovereign state to exist on this land was Israel under the Hasmonean dynasty prior to the Roman invasion in 63 BCE.