1. First off, it is an "action-at-a-distance" force, meaning that any change happening at one locality generates immediately an effect at other places.
That is, INFORMATION is spread at infinite speed throughout the universe.
Newton himself was deeply dissatisfied with this, and regarded his universal law of gravitation as an ad-hoc formula, that probably wasn't entirely right.
With Einstein's special relativity, physicists understood that information transmission speed CANNOT exceed the speed of light (a FINITE speed!), and thus, that in this crucial respect, Newton's law had to be false.
2. With Einstein's general theory of relativity, the interconnections of mass and space made for a fascinating solution:
Space is NOT like the rectangular box Newton envisaged it to be, within which matter resided without changing the box itself.
Rather, the presence of mass warps space(-time) itself, somewhat similar to that if you put a heavy ball on a linen sheet, you deform the linen sheet itself in that process.
3. Thus, if you are to calculate CORRECTLY the orbit for, say, a planet very close to a sun, the envisaged box structure of space, as Newton's theory presupposes, distorts your calculations because you neglect the spatial warping due to the presence of the sun.
This was, back in the 19th century, known as the anomaly of Mercury's orbit; the calculations simply didn't match the observations.
Einstein's theory of general relativity rectified that flaw.
4. Einstein's theory is entirely LOCAL, in the sense that a heavy object warps its local spatial region, and sends out information about its position&warp&mass at light speed (by means of yet unobserved gravitational waves).
5. In some sense, you could say that gravitation is no longer a force that acts directly upon an object; rather, gravitation acts upon space, and objects close to that warped region moves FREELY (i.e, without being influenced by a force), but in curved paths, rather than "straight lines".
Remember from Newton's first law that if an object is not under the influence of any force, it will move in a "straight line"; within general relativity, this holds as well, but because the space is warped/curved close to a massive object, that "straight line" (shortest distance between two points) will be a curved path instead (called a "geodesic")