Science is a method and program for understanding physical reality, a role formerly occupied by religious revelation such as the days of creation in Genesis, for example (I will focus on only one religion, Christianity, since I don't know the relationship between science and any other religion).
The Christian method for determining how the world works prior to the advent and rise of science was to trust ancient revelation on faith. We can pretty much assume that all Christians up until then were creationists inasmuch as there was no alternative hypothesis available.
Modern science was a reaction to that methodology. Science rejected faith as a means of understanding physical reality, and replaced it with rational skepticism and empiricism, an implicit repudiation of the Christian method.
This new way of knowing demonstrated that the church and its Bible were wrong. Galileo and his telescope, for example, proved that heavenly bodies were not the perfect orbs that the church had claimed when he saw the pockmarked surface of the moon, and that not everything revolved around the earth when he identified four moons orbiting Jupiter.
Pope Urban VIII made a great tactical error at that point, one which set the tone for the relationship between science and Christianity for centuries. Rather than commenting, "Look at how great our god is - more imaginative than we had suspected," he instead attempted to silence Galileo. Bruno was burned at the stake for suggesting that ours was a solar system among other solar systems in space.
This created such a chill for scientists that Copernicus waited until near death to publish his work on heliocentrism, and centuries later, Darwin worried bout the church's response to his work.
Today, most of the church has acquiesced to the scientists, and most theologians are calling Genesis allegory rather than incorrect. The remnant of creationists are still waging war on science. We see that every day we visit these threads. I already have this morning and a few times yesterday. "No evidence," "mere supposition," "information programmed into DNA," "macroevolution is impossible," "you can't prove your theories," "OK, make a cat evolve into a dog," etc.. We're all familiar with it.
So that is the relationship of Christianity to science today. The church has mostly given up the fight and even embraced the science contradicting its scriptures, with a shrinking remnant of creationists still resisting science even to the point of home schooling their children to prevent them from hearing about evolution.
And the fraction of Westerners self-identifying as Christians is shrinking as atheism is growing in some part due to science:
- "Although atheism might have been logically tenable before Darwin, Darwin made it possible to be an intellectually fulfilled atheist" - Richard Dawkins