What is Faith?

In terms of the word "faith," or belief in a deity, I thought I understood what it meant. But I've read some claims about faith that have left me unsure. I've generally understood it as belief in something even beyond reason and understanding. For example, I've often heard it said that there are myteries about God that we cannot understand, and need to take on faith, such as the question of why bad things can seem to happen to good people despite God being all-loving and good. God's plan is beyond human understanding and all that, and to a ceratin extent, I can understand that. From evangelicals I've met, "faith" seemed to refer to a feeling; they knew God existed, they could feel his presence, and they believed because of that.

But lately I have read statements from some very religious Christians that say human feelings are fallible, that they can be misleading, that people should be careful and not just trust their emotions. And I would agree, there is some truth to that. Unfortunately, what does that mean about faith? If feelings shouldn't be blindly trusted, but God is also beyond human comprehension...then why do people believe? What is their faith in God's existence based on?

I realize I am very likely creating a hodgepodge of different religious perspectives here, especially since I know I'm pulling things I've heard from Catholics, Evangelicals, and Fundamentalists. So I do see that one potential answer is simply that yes, in fact, you can trust your feelings, especially since the Fundamentalist claim that you can't seem to only be said in response to people who've questioned their own faith. Still, any thoughts?