Naturally, there will be those who say that's not so.

He didn't appear physically - but spiritually:

Small Excerpt:

Nothing about John would indicate that he was Elijah. Elijah had physically ascended "into heaven" in a "chariot of fire." And, everyone believed that the same Elijah who had disappeared into heaven was himself, personally going to return... possibly even in the same "chariot of fire" that he had used when he ascended up into heaven.

In what way could John the Baptist have been the return of Elijah? Certainly not literally. This apparent contradiction can be resolved by a statement made at the beginning of the Gospel of Luke where it explains that John went

"on before the Lord, in the spirit and power of Elijah." -Luke 1:17 (KJV)

Elijah had returned from heaven in the "spirit". John went "on before the Lord, in the spirit and power of Elijah."-Luke 1:17 (KJV) Viewed this way, both John and Jesus were right. The man named Elijah who had lived eight hundred years earlier had not literally, physically returned from heaven in the flesh as just about everyone expected. Instead, the fulfillment of the 'return of Elijah from heaven' prophecy had nothing to do with Elijah's physical body. It was the return of the same "spirit and power" of God that had animated Elijah eight hundred years earlier that had returned to also animate John the Baptist. The reality of Elijah's return was the appearance of yet another totally separate and distinct Prophet of God. (Yes, Jesus did refer to John as a Prophet.) This is the true meaning of "the return."...

[link to prophecy-fulfilled.com]