In 1948, the two sides went to war. When it ended, Gaza was controlled by Egypt and another area, the West Bank, by Jordan. They contained thousands of Palestinians who fled what was now the new Jewish home, Israel.
But then, in 1967, after another war, Israel occupied these Palestinian areas and Israeli troops stayed there for years. Israelis hoped they might exchange the land they won for Arab countries recognising Israel's right to exist and an end to the fighting.
Israel finally left Gaza in 2005 but soon after, a group called Hamas won elections and took control there. Much of the world calls Hamas a terrorist organisation. It refuses to recognise Israel as a country and wants Palestinians to be able to return to their old home - and will use violence to achieve its aims.
Since then, Israel has held Gaza under a blockade, which means it controls its borders and limits who can get in and out. Life for many of the 1.5 million Palestinians who live in the Gaza Strip is very difficult.
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 frequent power cuts.
Large numbers of people are unemployed because businesses can get very few of their products out of Gaza to sell, and people don't have much money to buy things.