Is there a force called gravity?

"Gravity really does exist," said Newton after the publication of his famous Universal Law of Gravitation in 1687. While the oft-told story of an apple falling on his head is apocryphal, what Newton did was to work out the mathematical law that governs the gravitational attraction between two bodies.

To make his concept of gravity universal, Newton needed a universe where everything needs to know where everything else is so that gravity can act with the appropriate amount of force. Accordingly, his concept of gravity is a beautiful synthesis between terrestrial and celestial phenomena that "abundantly serves to account for all the motions of the celestial bodies," reaching across the vast expanse of the universe. 

The law works with clockwork precession as long as the masses have low density and move slowly. For example, the Earth and other planets orbit the Sun because of the gravitational force exerted by the Sun.  

Despite the amazing success of the law, Newton was never completely satisfied with his theory. There are many anomalies it cannot explain satisfactorily. One of them is the mystery of "action-at-a-distance," a concept involving two bodies interacting with each other without being in physical contact. He even wrote to a colleague, telling him that any "competent thinker shouldn't believe his theory."

The others are: how is the force transmitted through space? How do planets know that they have to move in elliptic orbits around the Sun? Besides, unlike magnets that can attract as well as repel each other, why does gravity always pull?

Moreover, Newtonian gravity does not work well for objects with enormous mass density or objects moving with speeds comparable to the speed of light. It also cannot explain the observed bending of light. Nevertheless, how philosophically unsatisfying the theory is, gravity seems to be a force of some sort.

Enter Einstein into the equation. He trashed Newton and claimed that there is no such thing as "gravitational force." According to his Theory of General Relativity, published in 1915, gravity is a manifestation of the curving of the fabric of space-time by matter. Simply put, space―length, width, and height―becomes curved and time slows down in the presence of matter. 

The more the mass, the greater is the curving and slower the clocks will tick. This is why astronauts, who are moving very fast in space, age a little bit more slowly than people on Earth.