The flags of the Fatah and Hamas groups
Hamas and Fatah are the two biggest Palestinians groups who both have considerable support among Palestinians.
They are rivals and fought each other in the Gaza Strip in 2007.
Palestinian Authority President Mahmoud Abbas is from Fatah. His party was beaten by Hamas in the Palestinian elections in 2006.
Palestinian Authority President Mahmoud Abbas
President Abbas also heads the Palestinian Liberation Organisation (PLO), which is like an umbrella group for lots of Palestinian groups - though not Hamas.
Hamas, Fatah and the PLO want Israel to end its occupation and a country of Palestine to be created. But they don't agree on what this state should look like.
The PLO wants a state based on the occupied territories.
Hamas says it wants a state to include what is now Israel, although its leaders have also said it might accept an end to the occupation and the creation of a Palestinian state.
They also don't agree on how this should happen.
The PLO has signed peace agreements with Israel in the past and supports peace talks. Most of its members do not think violence is the way to achieve their goals.
Hamas argues it has the right to what it calls 'armed resistance'.
Countries like the UK and America say they won't talk to the group until they agree to stop attacking Israelis.
Although Hamas often makes headlines when there is fighting, it also organises things like schools and medical help in areas where Palestinian people live.
Israeli Prime Minister Benjamin Netanyahu
Israel is governed by a Prime Minister who leads a cabinet of Ministers.
There are many political parties in Israel and because of the electoral system Israel uses, a government is often made up of quite a few parties.
They also don't agree on what they should do about the Palestinians and what a future Palestinian state should look like.
The Palestinian Authority (PA) was set up in 1994 as part of the peace agreement between Israel and the PLO. It was created to govern Palestinians in the Palestinian controlled parts of the Occupied Territories.
The PA has a President, a Prime Minister, a cabinet and a legislative body known as the Palestinian Legislative Council (PLC).
Presidential elections were held in January 2005 and parliamentary elections in January 2006.