According to our current understanding of physics, traveling faster than the speed of light is not possible for objects with mass. The theory of relativity, proposed by Albert Einstein, sets the speed of light in a vacuum as an absolute cosmic speed limit. As an object with mass approaches the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach or exceed the speed of light.
That being said, there are some speculative concepts and ideas that have been explored in theoretical physics, such as wormholes or warp drives, which involve manipulating space-time to potentially achieve faster-than-light travel. However, these concepts are purely theoretical at this point, and we do not yet have the technological or scientific understanding to make them a reality.
As for how close we are to achieving faster-than-light travel, it's difficult to provide a precise answer. While scientific progress continues, it's important to note that our current knowledge and understanding of physics do not support the possibility of faster-than-light travel for objects with mass. Breakthroughs in fundamental physics or the discovery of new phenomena could potentially change our understanding in the future, but faster-than-light travel remains firmly in the realm of science fiction.