At the heart of modern physics lurks a terrible puzzle: the two main theories that describe the world we live in just won't fit together.
The force of gravity is described by Einstein's general theory of relativity (which celebrates its 100th birthday this year). General relativity says that space and time can be curved by massive objects.
The other two fundamental forces of nature (the electroweak force and the strong nuclear force), as well as the fundamental particles, are described by quantum physics. A main result in this context is Heisenberg's uncertainty principle, which implies that you can never determine the location and motion of particles at the same time with complete precision (more accurately, the classical concepts of position and momentum cannot coexist with perfect sharpness).
But if those particles have mass, then according to general relativity, their motion effects the shape of space and time. Putting both theories together implies that you can't determine the space and time in which particles exist and move. That's clearly a problem, and displays a significant incompatibility between relativity and quantum theory. Physicists are hard at work developing a unifying theory of quantum gravity, but it's proving to be very, very tricky. One contender is string theory, which has taken the radical step of giving up the fundamental notion of a "point" in space and time.