Hello Eardrum!
This is my first post - I have been snooping around here, then joined but never posted - but that General Relativty really spiked my interest!
General Relativity is actually one of those topics that one doesn't start until the end of a Physics degree, mortals have to attempt to understand special relativity first. A great book that will give you a good understanding without "dumbing down" the material to much is "The Elegant Universe" by Brian Greene. Get this book, it will get you up to speed about current theory.
You asked, what theory is prevalent amongst scientists. Currently if you study the very big (astrophysics) Relativity describes things so extremely well that astronomers will tend to ignore the science of the very small (quantum physics). Only recently is there a push to combine these theories into something called "String Theory" and even more weird is a thing called "M- theory". Still, Relativity, together with Quantum physics,reign supreme...for now.
Now, space curvature. Think of empty space as a huge table cloth. Completely smooth, no bumps, nice smooth table cloth. The table cloth is held at the ends, aloft. Now...put a heavy object in the middle, what happens? Well the heavy object (lets say a bowling ball) bends the table cloth doesn't it. So this is an ok analogy for the Sun, it bends the space around it. Now what is so interesting about space bending is that objects travelling on this bent space will travel akwardly, in fact the travelling object will travel not in a straight line but because its "path" is bent. Warped Space is another way to say...gravity.
Hold on minute, why does mass curve space time..hmm... I can't remember what I read..but I can get back to you. Wow, I don't think I helped
sorry!
Cheers