Faith in a Scientific Worldview

Should faith impact scientific understanding? Can scientific understanding diminish faith?

Some people think that science and faith deal with different aspects of inquiry, and do not overlap with or contradict each other (Stephen Jay Gould’s non-overlapping magisteria). Others think that the two do overlap in practice, and in the case of a conflict, one should be preferred to the other.

Do faith and science influence each other? Should they? What should one do when the two disagree?