This can be divided into four periods as:
In Islam the formation of government is based on council or on nomination. It is not based on any alleged Divine power held by the rulers. After the Prophet (PBUH), the companions elected Hadrat Abu Bakr (RA) as the first Caliph, and he ruled for two and a half years. On his deathbed he nominated Umar (RA) the second Caliph who ruled for about 10 years. Hadrat Umar (RA) appointed a six-man committee for the selection of the third Caliph. Uthman (RA) was then elected out of these six; he ruled for 12 years. After him, Ali (RA) was elected as the fourth Caliph, he ruled for nearly 4 years. The period of these four Rightly guided Caliphs is called Khilafat-e-Rashidah.
Then the Ummayads, a line of the family of Abdul Munaf came to power. The first of these was Muawiyah (RA); his seat of governance was Damascus, Syria. This dynasty ruled for nearly a century. Then the Abbasids, a line of the family of Abdul Muttalib took power and their center of power was Baghdad, Iraq. Then the caliphate of central governance ended and the power transferred to the provincial rulers. Subsequently Turkey became the center of the Muslim political power and the reign of the Uthmanids commenced. This caliphate came to an end following the defeat of the Germans in the First World War; the Turks were allied with Germany. Since then the political power of Muslims is with independent Muslim states.