1 - Abu Bakr bin Abu Qahafa (RA)
2 - Umar bin al-Khataab (RA)
3 - Uthman bin Afaan (RA)
4 - Ali ibn Abi Talib (AS)
They are titled Al Khulafa' ar-Rashideen - The Rightly-guided Leaders.
Subsequent leaders were also called Khalifs as they had rulership of the whole Islamic Ummah (nation/peoples). Each khalif was titled 'Ameer al-Mu'mineen' (Commander of the Faithful) even though this title was given to Imam Ali by the Prophet exclusively. The Khilafah system ended with the end of the Ottman empire. There can be no more Khalifate until a new Islamic empire is re-born.
The Khalifate issue is quite controversial as the purpose of leadership was to manage the Muslim Ummah, yet the Prophet (SAW) did not commission a Khalif after him or organise a method of choosing the Khalifah. The Shia Muslims argue otherwise and state that the Prophet (SAW) chose Ali ibn Abi Talib (AS) to be the leader after his departure and his sons after him, as an order by Allah. This did not happen and as you can see in the list above Imam Ali ended up being the fourth khalif. There were five main methods of becoming khalif:
- Election by a small number of elite people
- Passing of leadership from Khalif to friend
- Passing of leadership from Khalif to son/decendant
- Murder of the khalif
- War imposed on the khalif by rebels (rebellion)