First of all, it is necessary to know that the Quran speaks in a general way. All the general statements of the Quran are explained in detail in the traditions of the Holy Prophet (s) and his household. Considering this point, we can find two sets of verses from which we understand the existence of the Imam of Age (atf) and his reappearance:
1. There are verses in the Quran which explains the necessity of divine proof or a divine authority among people. For example, God said to the Holy Prophet of Islam (s): "You are only a warner and (there is) a guide for every people." This verse and the narrations which interpret it affirm and stress, in a general way, the permanent existence of divine leaders among people on earth.
2. There are verses in the Quran which give the good news (glad tiding) that the righteous, the weakened and the believers will rule the earth. For example, the Quran says: "And certainly We wrote in the Book after the reminder that (as for) the land, My righteous servants shall inherit it." Else where in the Quran, God, the Exalted, promises that the righteous servants will come to power and peace and security will prevail on earth and they will help the religion of God to spread all over he world.
The narrations which interpret the verses have declared Imam Mahdi (atf) as the living manifestation of God's hujjah who will reappear one day and fill the world with justice.
The reappearance of an awaited savior, who will come one day and will fill the world with equity and justice, is an established belief accepted by all religions and denominations. The difference is about the manifestation of the savior and the characteristics which he bears. However, Shia believes that Imam Mahdi – may Allah hasten his reappearance – is the savior and the global reformer.
Since the Quran is based on strong natural and rational arguments and proofs, it serves as the best document and evidence to prove a scientific and religious point. It is necessary to note in the very beginning that the Quran speaks most often in a general way, and in order for us to understand the Quranic verses and traditions, we must turn to experts of the Quranic sciences i.e. the infallible Imams (a.s). In other words, the task of explaining and elaborating on the Quranic verses has been relegated to divine authorities.
In response to the foregoing question, we will suffice only to mentioning and briefly explaining a few relevant verses of the Quran and some sayings of the Infallibles (a.s) to make our point clear. At any rate, we can find two categories of Quranic verses from which we clearly understand the existence of the Imam of Age (atf) and his reappearance:
1. Verses which explains the necessity of divine proof or a divine authority among people.
2. Verses which give the good news (glad tiding) that the righteous, the weakened and the believers will rule the earth.
1. Verses stressing the necessity of divine authority among people:
According to the Quran, the earth will never be empty of a person who has arisen with the proof of God. God, the Almighty, has chosen a suitable individual for every nation so that he guides them in the right path and enable them to attain the desire perfection. He says:
"إِنَّما أَنْتَ مُنْذِرٌ وَ لِكُلِّ قَوْمٍ هاد"
"You are only a warner and (there is) a guide for every people."
Therefore, at all times in every nation, there is always a warner of Allah. At all times, there is always a guide among people who has been chosen by God. Imam Sadiq (a.s.) said in the interpretation of the above verse:
"At every time, there will an Imam from our family who would guide people to what the Messenger of Allah brought down (i.e. the religion of Islam)."
It is inferred from the foregoing Quranic verse and tradition that it is necessary that there be a divine authority as a guide at every time and age.
Another argument indicating the necessity of an infallible leader in society is that the Quran needs an interpreter to interpret the Quran and there is no one other than an infallible imam (leader) to know the meanings and features of the verses of the Quran including the explicit and ambiguous verses. Hence, on the sole basis of reason, there must be an infallible Imam after the Messenger.
Concerning the necessity of the existence of an infallible imam, Imam Reza (a.s.) says:
"The earth will never be devoid of a hujjah (divine proof) even for a wink of an eye and if it remains devoid, it will sink into itself along with its inhabitants."
The infallible imams are a source peace, tranquility and security of the world; they are intermediaries between God and His creatures. It is because of them that divine bounties and blessings are bestowed upon humans. If it were not for their existence, the earth would sink into itself and swallow its inhabitants.
As for who the manifestation of infallible leader in the present age and his traits, there are many narrations which clearly state that he is the son of Imam Hasan Askari (a.s.), the Mahdi – may Allah hasten his reappearance.
2. Verses which give the good news (glad tiding) that the righteous, the weakened and the believers will rule the earth:
The reappearance of the Imam Mahdi can be proven with reliance on many verses from the Quran. These verses focuses on the glad tiding to the righteous servants of God and to the weakened (mustaz'afeen) that they will be able to restore their right and reach power and that they shall be enabled to establish a single global government on the basis of truth, justice and domination of Islam over all religions and schools. The Holy Quran also says that some other heavenly books also contains the same glad tiding: "And certainly We wrote in the Book after the reminder that (as for) the land, My righteous servants shall inherit it."
The Quran ascribes the glad tiding to the will of God: "And We desired to bestow a favor upon those who were deemed weak in the land, and to make them the Imams, and to make them the heirs." This verse of the Quran, which has also been interpreted by many narrations, gives the good news of reappearance and affirms our point in this regard.
In another verse, God, the Almighty, terms the government of the believers and righteous as a "divine promise" to his faithful servants giving the good news of peace and security:
"Allah 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; that He will establish in authority their religion - the one which He has chosen for them; and that He will change (their state), after the fear in which they (lived), to one of security and peace: 'They will worship Me (alone) and not associate aught with Me. 'If any do reject Faith after this, they are rebellious and wicked."
The sayings and narrations from the Infallibles (a.s) have applied this verse to the Imam of Age (atf) and his companions.
Awaiting for the reappearance which is by itself an independent topic and implies the "existence" and "reappearance" of the Imam of Age (atf) have been mentioned in the Quran and the narrations of the Infallibles (a.s.). "و ارتقبوا انی معکم رقیب"
In a tradition from Imam Reza (a.s.) on the meaning of the above verse, "waiting for reappearance" has been considered a cause of happiness and peace.
What is inferred from the verses and narrations is that, based on divine grace and wisdom, there have always been divine leaders warning people and giving them glad tidings. God has made their existence on earth eternal. Imam Mahdi, may Allah hasten his reappearance, is the existing divine authority and is leading the world and he will reappear soon.
 - For further information in this regard, see: Index: The Imam of Time (atf) and Religions, question 1428 (site: 1631).
 - Hadith Thaqalayn, Mustadrak Hakim, vo.3, pg. 148, Darul Ma'refah Publications, Beirut.
 - Al-Ra'ad, 7.
 - Behar al-Anwar, vol.23, pg. 5, ("و فی کل زمان امام منا یهدیهم الی ماجاء به رسول الله (ص)".)
 - Banuye Isfahani, Sayyida Nusrat Amin, Makhzan al-Irfan fi Tafsir al-Qur'an, vol.3, pg. 39, Explanation of verse 44, al-Nahl.
 - Behar al-Anwar, vol.23, pg. 29, There are similar hadiths in the same book.
 - Go to Behar al-Anwar, vol.23, pg. 56 to find traditions which indicate the necessity of a permanent heavenly leader on earth.
 - See: Muntakhab al-Athar, Najm al-Thaqib, Behar al-Anwar, vol.23.
 - Al-Anbiya, 105: "و لقد کتبنا فی الزبور من بعد الذکر ان الارض یرثها عبادی الصالحون"
 - Al-Qasas, 5.
 - Al-Noor, 55
 - See: Omid Sabz, pg. 34, Farzi, Muhammad Ali.
 - "And watch, surely I too am watching with you." Hud, 93
 - Al-Mizan, pg. 394 – 394.
 - For further information in this regard, see: 'Maw'ud Shinasi wa Pasokh be Shobahat", Rezwani, Ali Asghar, pg. 287 – 298.