Jesus was the Messiah.

(Although according to the Quran he was also just a messenger of Allah, and it is not at all clear what the Quran means by the word "Messiah.")

For a good discussion of this see Gabriel Said Reynolds's YouTube video on this.

(And remember) when the angels said: O Mary! Lo! Allah giveth thee glad tidings of a word from him, whose name is the Messiah, Jesus, son of Mary. 3:45

The Messiah, Jesus son of Mary, was only a messenger of Allah. 4:171

The Messiah will never scorn to be a slave unto Allah. 4:172

The Messiah (himself) said: O Children of Israel, worship Allah, my Lord and your Lord. 5:72

he Messiah, son of Mary, was no other than a messenger, messengers (the like of whom) had passed away before him. 5:75

But he was neither killed nor crucified.

(It just looked that way.)

And because of their saying: We slew the Messiah, Jesus son of Mary, Allah's messenger - they slew him not nor crucified him, but it appeared so unto them; and lo! those who disagree concerning it are in doubt thereof; they have no knowledge thereof save pursuit of a conjecture; they slew him not for certain. But Allah took him up unto Himself. 4:157-8

Allah saith: O Jesus, son of Mary! Remember ... how I restrained the Children of Israel from (harming) thee. 5:110

Wikipedia: Islamic views on Jesus's death

The baby Jesus spoke like an adult.

Then she [Mary] pointed to him [the baby Jesus]. They said: How can we talk to one who is in the cradle, a young boy? He [Jesus] spake:

Lo! I am the slave of Allah. He hath given me the Scripture and hath appointed me a Prophet, And hath made me blessed wheresoever I may be, and hath enjoined upon me prayer and almsgiving so long as I remain alive, and (hath made me) dutiful toward her who bore me, and hath not made me arrogant, unblest. Peace on me the day I was born, and the day I die, and the day I shall be raised alive! 19:29-33

He [Jesus] will speak unto mankind in his cradle. 3:46

Allah saith: O Jesus, son of Mary! Remember My favour unto thee and unto thy mother; how I strengthened thee with the holy Spirit, so that thou spakest unto mankind in the cradle as in maturity. 5:110

When Jesus was a child, he made a clay bird fly away by breathing on it.

Lo! I [Jesus] fashion for you out of clay the likeness of a bird, and I breathe into it and it is a bird, by Allah's leave.3:49

Allah saith: Allah saith: O Jesus, son of Mary! Remember ... how thou didst shape of clay as it were the likeness of a bird by My permission, and didst blow upon it and it was a bird by My permission. 5:110

Jesus sent a food-filled table down from heaven to feed his disciples

Jesus, son of Mary, said: O Allah, Lord of us! Send down for us a table spread with food from heaven, that it may be a feast for us ... Allah said: Lo! I send it down for you. 5:114-15