It is said very clearly in the Bible that the Prophet Elijah, who never died, will return a little before the Second Coming of Christ.  In the same way that the disciples in Jesus' time were confounded because they didn't see Elijah coming before the Messiah (Christ), so many modern Christians are confused believing that Elijah was John the Baptist. This prophet was not Elijah, as he himself clearly states in John 1: 21.

    If John the Baptist really was Elijah he would not have denied it.  John the Baptist came in the spirit and power of Elijah, as says Luke 1: 17, and that is why Jesus said that he was "the Elijah"  that was going to come before the Lord in his First Advent.  Nevertheless, even that Jesus himself said that John the Baptist was the "Elijah-like" prophet that was to come in his First Advent, still near the Second Coming of the Lord, the true Elijah shall come again. Let us see what Jesus said regarding that issue.

            "10 And his disciples asked him, saying:  Why then say the scribes that Elias
        must first come?  11 And Jesus answered and said unto them, Elias truly shall
        first come, and restore all things. 12 But I say unto you, that Elias is come already,
        and they knew him not, but have done unto him whatsoever they listed. Likewise
        shall also the Son of man suffer of them.  13 Then the disciples understood that
        he spake unto them of John the Baptist."      (Matthew 17: 10-13.)

    Everyone I know interprets from this passage that John the Baptist was the Elijah that was prophesied.  But as far as I know no one interprets from that passage that Jesus said clearly that Elijah shall come (future) and shall restore (future again) all things.  Note that when referring to the true Elijah, Jesus speaks in future tense (shall come; shall restore), but when referring to John the Baptist he speaks in the past tense (is come already; knew him not).
     From this passage we can deduce, without forcing the argument, that Christ admitted that Elijah was yet to come.  But this is not all.  Let's go on to read the original prophecies; lets read Malachi 3:1, where John the Baptist's mission during the First Coming of the Lord, is prophesized, and later let's read Malachi 4: 5-6 where Elijah's coming before the Second Coming of the Lord, is prophesized.

            "Behold, I will send my messenger, and he shall prepare the way before me: and
       the Lord, whom ye seek, shall suddenly come to his temple…" (Malachi 3:1)

    In this verse the one whose coming and mission Malachi is talking about is called "my messenger".  He doesn't call him Elijah. Besides, Malachi says very clearly that the messenger's mission is to prepare the way before Christ, and that after such a pacific mission is that Christ would come to his temple.  The prophet talks of the "messenger" as a man who is going to come during the time that Jesus would enter in the Second Temple. A messenger that was going to come in a time in which people could still enter in the Second Temple, because it was not destroyed. (The Temple was destroyed in year 70 AD).
    This messenger didn't come in a mission of punishment, but in a mission of announcing and preparing the pacific First Coming of Our Lord .  The other prophecy is very different. Let us see.

            "Behold, I will send you Elijah the prophet before the coming of the great
        and dreadful day of the LORD.  He shall turn the heart of the fathers to the children,
        and the heart of the children to their fathers, lest I come and smite the earth with
        a curse."                                                                             (Malachi 4: 5-6.)

    Here we see a very different picture.  First he calls the messenger by his personal name, he calls him Elijah.   Second, in order to avoid any doubt he clarifies that he refers to "the prophet", in case that anyone could think of another Elijah.  Third, Malachi specifies that Elijah's mission is going to take place before the coming of the great and dreadful day of the LORD.  That description does not depict the First Coming of Christ.  His First Coming was an event extremely pacific, devoid of dramatics and dreadfulness, contrary to his Second Coming, which will be full of both dramatics and dreadfulness.  In his First Coming, Christ didn't come to smite or destroy the earth, but instead to save it, to suffer for it.  Therefore Malachi cannot be talking in this passage about John the Baptist during the First Coming of Christ, but about Elijah before the Second Coming of the Lord.
    By the study of both passages we can conclude that Malachi is talking about two different individuals who were going to have a similar mission ( to be forerunners), each one in very different times and circumstances.  The first one is John the Baptist, in the time of Christ's First Coming; the second one is Elijah the Prophet, in latter times, near the Second Coming.  When Jesus identifies John the Baptist in Matthew 11:10, he identifies him using the words found in Malachi 3:1, never the words used in Malachi 4: 5-6. Let's see:

            "For this is he, of whom it is written: 'Behold, I send my messenger before
        thy face, which shall prepare thy way before thee'."       (Matthew 11:10)

    This passage from Matthew confirms that it is Malachi 3:1 the one that talks about John the Baptist and not Malachi 4:5-6.