Based on our current understanding of physics, we expect the Sun to continue pretty much unchanged for another 3 to 4 billion years as it fuses hydrogen into helium. It will then grow - abruptly! - into a red giant, and burn for perhaps another billion years, fusing helium into heavier elements like carbon and oxygen.
After that, it'll be all downhill, and the Sun will begin to cool down and collapse into a white dwarf. We don't really know how much longer it can continue as a white dwarf before it finally fades into a brown dwarf.
For us here on Earth, that's pretty academic, since the Earth itself will probably have been incinerated when the Sun expands into a red giant. Unless, of course, we move the Earth to another, younger, star. By the time we need to do that, we'll know how....