After the 1948 war, Jordan took control of the West Bank and Egypt took control of the Gaza Strip.
The city of Jerusalem was split, with Jordan taking control of East Jerusalem while West Jerusalem was in Israel.
Israel captured the West Bank, Gaza Strip and East Jerusalem during another war in 1967.
Since then, Israel has set up many Jewish settlements - communities, some tiny, some as big as small towns - in both the West Bank and the Gaza Strip.
These settlements are considered illegal under international law, although Israel does not agree with this.
Living under occupation
Palestinians in the West Bank, including East Jerusalem, have lived under Israeli occupation since 1967.
Human rights groups have recorded widespread abuses by Israeli soldiers of Palestinians. For example, the Israeli army has put up lots of check points and roadblocks between villages and towns.
Palestinians say it makes it much harder to visit friends and family or get to work, school or hospital. Some Palestinians compare the restrictions on their lives to being in a prison.
The Israeli government says the checkpoints are to protect settlers and to prevent potential Palestinian suicide bombers from harming Israelis.
The Gaza Strip
Life for the many of the 1.5 million Palestinians who live in the Gaza Strip is difficult.
It is a narrow piece of land along the Mediterranean coast and access to it is very limited. It is fenced in and Israel controls its coastline and all the entry and exit crossings into Israel. There is another crossing point into Egypt. There is no working airport.
Because access is so restricted, not many goods get into or out of Gaza.
Food is allowed in, but aid agencies say families are not eating as much meat or fresh vegetables and fruit as they used to. There are often power cuts.
Large numbers of people have lost their jobs because businesses can get very few of their products out of Gaza to sell, and people don't have much money to buy things.
Israel withdrew all of its settlers and troops from the Gaza Strip in 2005.