The Verse of Istikhlaf and the Caliphate

Allah (swt) says in the Holy Quran: 

"Allah has promised those who have believed among you and done righteous deeds that He will surely grant them succession [to authority] upon the earth just as He granted it to those before them and that He will surely establish for them [therein] their religion which He has preferred for them and that He will surely substitute for them, after their fear, security, [for] they worship Me, not associating anything with Me. But whoever disbelieves after that - then those are the defiantly disobedient." (24:55)

Allah (swt) is placing a condition for succession and authority in that he will establish authority for those who believe and who have done righteous deeds. Now we know that Allah (swt) granted Abu Bakr (ra) the authority over Muslims, granted him power, security, victory and established the religion through him and as well through the other Caliphs (ra). 

Another verse in the Quran has a similar connotation: 

"Muhammad is the Messenger of Allah ; and those with him are forceful against the disbelievers, merciful among themselves. You see them bowing and prostrating [in prayer], seeking bounty from Allah and [His] pleasure. Their mark is on their faces from the trace of prostration. That is their description in the Torah. And their description in the Gospel is as a plant which produces its offshoots and strengthens them so they grow firm and stand upon their stalks, delighting the sowers - so that Allah may enrage by them the disbelievers. Allah has promised those who believe and do righteous deeds among them forgiveness and a great reward.

As for the Imams of the Ahl Al-Bayt (as), only 2 out of the 12 of the Imams (as) had authority over the Muslims. As stated before, the verse places a condition for succession and authority not on infallibility, but for the people who believe and do righteous deeds: "Allah has promised those who have believed among you and done righteous deeds". This is a promise for the believers and not just to 12 Infallible Imams as the 12r Shia erroneously claim. To continue, the verse also states that Allah (swt) will: "He will surely substitute for them, after their fear, security." The 12rs claim that their imams were in taqiyyah due to fear and persecution, but as we see, Allah (swt) states the opposite in the verse. 

In fact, Imam Ali (as) alludes to this in sermon 145 of Nahjul Balagha to Umar (ra): 

"In this matter, victory of defeat is not dependent on the smallness or greatness of forces. It is Allah's religion which He has raised above all faiths, and His army which He has mobilized and extended, till it has reached the point where it stands now, and has arrived its present positions. We hold a promise from Allah, and He will fulfill His promise and support His army. The position of the head of government is that of the thread for beads, as it connects them and keeps them together. If the thread is broken, they will disperse and be lost, and will never come together again. The Arabs today, even though small in number are big because of Islam and strong because of unity."

In its Sharh , Ibn Maitham says:
ثم وعدنا بموعود و هو النصر و الغلبه و الاستخلاف فى الارض كما قال وعد الله الذين آمنوا منكم و عملوا الصالحات ليستخلفنهم فى الارض كما استخلف الذين من قبلهم الايه، و كل وعد من الله فهو منجز لعدم الخلف فى خبره
"We hold a promise from Allah and that is the promise of success, and overpowering and istikhlaf, as Allah said in Quran : "God has promised, to those among you who believe and work righteous deeds, that He will, of a surety, grant them in the land, inheritance (of power), as He granted it to those before them" and Allah's promise will come true definitely."  

Imam Ali (as) is telling Umar (ra) not to worry because Allah (swt) will fulfill his promise as he has promised in the Quran. Further, Imam Ali (as) declared the army of Umar (ra) to be the army of Allah (swt).  

This also fits in with the Prophecy from the Prophet (pbuh) who stated:

"The khilaafah after me in my Ummah will last for thirty years. Then there will be kingship after that."Reported in the Musnad Imaam Ahmad, by at-Tirmidhi, Musnad Abi Ya'laa, and Ibn Hibbaan;  "Saheeh"by Imaam al-Albaani (ra)

"Imam Ahmad, Abu Dawud, At-Tirmidhi and An-Nasa'i have all reported from the hadith of Sa'id ibn Juhman, from Safinah - the mawla of the Messenger of Allah sallallahu 'alayhi wa sallam, that the Messenger of Allah sallallahu 'alayhi wa sallam said: "The Succesorship (Al-Khilafah) after me will last for thirty years. Then kingship will appear." -"Sahih"-Related by Abu Dawud, At-Tirmidhi, Authenticated by At-Tabari in his I'tiqad, and Al-Hafidh ibn Hajr in Fath-al Bari. 

"The Prophethood will remain amongst you for as long as Allaah wills it to be. Then Allaah will raise it when He wills to raise it. Then there will be the khilaafah upon the Prophetic methodology. And it will last for as long as Allaah wills it to last. Then Allaah will raise it when He wills to raise it. Then there will be biting kingship, and it will remain for as long as Allaah wills it to remain. Then Allaah will raise it when He wills to raise it. Then there will be tyrannical (forceful) kingship and it will remain for as long as Allaah wills it to remain. Then He will raise it when He wills to raise it. Then there will be a khilaafah upon the Prophetic methodology."-Silsilah as-Saheehah of Imaam al-Albani; "Sahih"

In fact, the Shia hadiths that allude this verse refers to their Imams are weak:

الْحُسَيْنُ بْنُ مُحَمَّدٍ عَنْ مُعَلَّى بْنِ مُحَمَّدٍ عَنِ الْوَشَّاءِ عَنْ عَبْدِ اللَّهِ بْنِ سِنَانٍ قَالَ سَأَلْتُ أَبَا عَبْدِ اللَّهِ ع عَنْ قَوْلِ اللَّهِ جَلَّ جَلَالُهُ- وَعَدَ اللَّهُ الَّذِينَ آمَنُوا مِنْكُمْ وَ عَمِلُوا الصَّالِحاتِ لَيَسْتَخْلِفَنَّهُمْ فِي الْأَرْضِ كَمَا اسْتَخْلَفَ الَّذِينَ مِنْ قَبْلِهِمْ قَالَ هُمُ الْأَئِمَّةُ
“I asked Abaa `Abd Allaah (عليه السلام) about the words of Allaah, jalla jalaalahu, «Allaah has promised those of you who believe and do righteous deeds that He will surely make you successors in the land, even as He made those who were before them successors» (24:55). He (عليه السلام) said: ‘They are the Imaams’”

Source:
• Al-Kulayni, Al-Kaafi, vol. 1, pg. 193 - 194, hadeeth # 3
  Grading:
• Al-Majlisi said this hadeeth is Da`eef `ala Mashhoor (A Famous Weak hadeeth)
  --> Mir'aat Al-`Uqool, vol. 2, pg. 351

This one is weak as well, actually VERY Da'eef.

محمد بن إبراهيم النعماني، قال: حدثنا أحمد بن محمد بن سعيد بن عقدة، قال: حدثني أحمد ابن يوسف بن يعقوب الجعفي أبو الحسن، من كتابه، قال: حدثنا إسماعيل بن مهران، قال: حدثنا الحسن بن علي ابن أبي حمزة، عن أبيه و وهيب، عن أبي بصير، عن أبي عبد الله (عليه السلام)، في قوله: وَعَدَ اللَّهُ الَّذِينَ آمَنُوا مِنْكُمْ وَ عَمِلُوا الصَّالِحاتِ لَيَسْتَخْلِفَنَّهُمْ فِي الْأَرْضِ كَمَا اسْتَخْلَفَ الَّذِينَ مِنْ قَبْلِهِمْ وَ لَيُمَكِّنَنَّ لَهُمْ دِينَهُمُ الَّذِي ارْتَضى‏ لَهُمْ وَ لَيُبَدِّلَنَّهُمْ مِنْ بَعْدِ خَوْفِهِمْ أَمْناً يَعْبُدُونَنِي لا يُشْرِكُونَ بِي شَيْئاً، قال: «نزلت في القائم و أصحابه».
About the saying (of Allah) «God has promised those of you who believe and do righteous deeds that He will surely make you successors in the land, even as He made those who were before them successors, and that He will surely establish their religion for them that He has approved. for them, and will give them in exchange, after their fear, security: 'They shall serve Me, not associating with Me anything.'» (24:55). He (عليه السلام) said: ‘This was revealed for Al-Qaa’im and his companions’

Source:
• Al-Nu`maanee, Al-Ghaybah, ch. 13, pg. 240, hadeeth # 35

This one is Da`eef as well.

محمد بن العباس: عن الحسين بن محمد، عن معلى بن محمد، عن الوشاء، عن عبد الله بن سنان، قال: سألت أبا عبد الله (عليه السلام) عن قول الله عز و جل: وَعَدَ اللَّهُ الَّذِينَ آمَنُوا مِنْكُمْ وَ عَمِلُوا الصَّالِحاتِ لَيَسْتَخْلِفَنَّهُمْ فِي الْأَرْضِ كَمَا اسْتَخْلَفَ الَّذِينَ مِنْ قَبْلِهِمْ، قال: «نزلت في علي بن أبي طالب، و الأئمة من ولده (عليهم السلام)».
وَ لَيُمَكِّنَنَّ لَهُمْ دِينَهُمُ الَّذِي ارْتَضى‏ لَهُمْ وَ لَيُبَدِّلَنَّهُمْ مِنْ بَعْدِ خَوْفِهِمْ أَمْناً، قال: «عنى به ظهور القائم (عليه السلام)».
I asked Abaa `Abd Allaah (عليه السلام) about the words of Allaah (عَزَّ وَ جَلَّ) «Allaah has promised those of you who believe and do righteous deeds that He will surely make you successors in the land, even as He made those who were before them successors» (24:55). He (عليه السلام) said: ‘This was revealed for `Alee bin Abee Taalib, and the Imaams from his children (عليه السلام)’. «and that He will surely establish their religion for them that He has approved. for them, and will give them in exchange, after their fear, security» He (عليه السلام) said: ‘(This) means for his Al-Qaa’im’s appearance”

Source:
• Al-Astrabaadee, Ta'wil Al-Aayaat, pg. 365