There are many interpretations and misconceptions about how Muslims view Jesus. The current, accepted, scholarly interpretation claims that Muslims believe Jesus was a prophet, but he did not possess the divinity moniker, did not die on the cross, and did not atone for the sins of mankind.
Muslims do not believe that Jesus was divine, but that he was merely a sinless, messenger of God. According to Muslims, the divinity association only gets in the way of knowing and understanding Jesus' message. That message is to live a good life and to accept God's guidance. You don't need Jesus as God to act as an intermediary. Muslims believe that a relationship with God is between an individual and God, not Jesus.
Muslims do not believe in Jesus' redemptive sacrifice either (Jesus crucified to redeem us from the sins of Adam and Eve). According to Islamic canon, Jesus ascended to heaven prior to his body being crucified because there can't be redemption with someone who is sinless. Christians claim that Jesus had to die to be sinless, but Muslims assert that Jesus was already sinless, and didn't need to participate in the sacrificial redemption; instead, he ascended straight to heaven without being part of the crucifixion procession. The Qur'an is specific about his live ascension:
That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah";- but they killed him not, nor crucified him, but so it was made to appear to them, and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not:-Without the redemptive quality, there can be no atonement from Jesus. According to Muslims, atonement is done through accepting God and living a sinless and ideal life using Jesus' guidance and teachings. This achieves salvation. Since Muslims do not adhere to a specific set of beliefs such as the Crucifixion and it's redemptive message, salvation is achieved through good behavior here on Earth.
Nay, Allah raised him up unto Himself; and Allah is Exalted in Power, Wise;-
—Qur'an sura 4 (An-Nisa) ayat 157-158
Christians believe that Jesus had to die on the cross and ascend to heaven to atone for our original sin (breaking the original sin of Adam and Eve). Muslims believe that Jesus was sinless, never died and ascended to heaven alive with the intention of returning, and never atoned for our sins. Aside from these differences, Christian and Muslim interpretations of Jesus are similar.