Actually it started in 1953 when the US instigated a coup to overthrow a popularly elected prime minister to install a US friendly but wildly unpopular Shah who proceeded to brutalize the people of Iran in an effort to kowtow to the US and act as their puppet/lackey until the Iranian people were fed up enough and the popular revolt overthrew the Shah and installed the Ayatollah in 1979. There is a very legitimate reason why the moderate people of Iran are pissed at the US when they've been forced to live under a religious zealot extremist government instead of the moderate secular government the US overthrew because they were going to nationalize their oil industry to prevent the British (BP) from stealing their oil wealth.
The hostages taken in 1979 were a direct result of the US meddling with Iran.
The war today is more of a proxy war with China (like Venezuela). Iran and Venezuela provided China with the majority of its oil. By meddling there we cripple the Chinese economy and gaining in other ways that are far less visible to us regular folks. China is trying to position itself as the next economic superpower to take the spot the US has held for the last 60+ years. They can't quite back things up militarily across the globe but economically, diplomatically, and technologically? They're getting there.