In a tradition upon whose authenticity all Muslims agree, the Holy Prophet has said:
"Even if the entire duration of the world's existence has already been exhausted and only one day is left before Doomsday (Day of judgment), Allah will expand that day to such a length of time, as to accommodate the kingdom of a person out of my Ahlul-Bayt who will be called by my name. He will then fill out the earth with peace and justice as it will have been full of injustice and tyranny before then."
Sunni Reference: Sahih Tirmidhi, V2, P86, V9, P74-75 (There are many more.)
The context of the above precious tradition informs the golden divine promises will take place, sooner or later, one way or another, as mentioned in most of the Shi'ite and Sunnit sources.
In a tradition the Holy Prophet said to the Commander of believers, Ali, that:
"There will be twelve Guides (Imams) after me, the first of whom is you, O' Ali, and the last one will be the 'Support' (al-Qa'im), who with the grace of Allah, will gain victory over the whole east and west of the world."
The occultation of the twelfth Imam is divided into two parts: the first, the minor occultation (ghaybat al-Sughra) which began in 259/873 and ended in 329/939, lasting about seventy year. On that period, people were in contact with him through four special deputies. That period served as preparing people for the absence of Imam. The second, the major occultation which commenced in 329/939 and will continue as long as God wills it. There is no special deputy in direct contact with him in this period, and Muslim scholars are regular deputies of him at this time without having ability to see him.
imam mahdi(as)
Imam Mahdi (AS) said:
"Rest assured that no one has a special relationship with Allah.Whoever denies me is not from my (community). The appearance of the Relief (al- Faraj) depends solely upon Allah. Therefore those who propose a certain time for it are liars. As to the benefit of my existence in occultation, it is like the benefit of the sun behind the clouds where the eyes do not see it. Indeed, my existence is an amnesty for inhabitants of the earth. Pray much to Allah to hasten the Relief, for therein also lays the release from your sufferings."
source : tebyan