What kind of fundamental interaction is gravitation? Einstein showed that gravitation is not a force but a effect caused by curvature of space time.
Then why does theories of quantum gravity treats gravitation as one of fundamental force?
 A: Ever after Maxwell unified electricity and magnetism, the goal of unification is a holy grail for theoretical physics, for all forces. 
The  macroscopic forces of electricity and magnetism emerge from the underlying quantized level of nature, photons, electrons and all the elementary particles in the standard model table enter with fields in quantum field theory. The emergence of the classical field , and thus the classical forces, from the underlying quantum level, can be shown mathematically. At the quantum level the word "force" just means interactions. 
One is looking for theories then  which at the quantum level have interactions from which macroscopically the observed forces are seen and classified. The weak and the strong are short range "forces" which were discovered with the advent of nuclear energy and the use of accelerators. They are called forces because at the quantum level they are modeled similar to the way the electromagnetic interactions are modeled.
It is not surprising that theoretical physicist attempted to quantize gravity, expecting the General Relativity framework to emerge mathematically from the underlying quantized gravity. Effective gravitational quantum field theories have been used in the current cosmological model of the Big Bang without contradictions and confirming observations.
At present the best candidates I see for unification of all four forces ( two of them long range, two short range) at the elementary particle level are string theory models:
>Strings and gravitons

The simplest case to imagine is a single string traveling in a flat spacetime in d dimensions, meaning that it is traveling across space while time is ticking, so to speak. A string is a one-dimensional object, meaning that if you want to travel along a string, you can only go forwards or backwards in the direction of the string, there is no sideways or up and down on a string. The string can move sideways or up and down in spacetime, though, and as the string moves around in spacetime, it sweeps out a surface in spacetime called the string worldsheet, a two-dimensional surface with one dimension of space and one dimension of time.
The string worldsheet is the key to all the physics of the string. A string oscillates as it travels through the d-dimensional spacetime. Those oscillations can be viewed from the two-dimensional string worldsheet point of view as oscillations in a two-dimensional quantum gravity theory. In order to make those quantized oscillations consistent with quantum mechanics and special relativity, the number of spacetime dimensions has to be restricted to 26 in the case of a theory with only forces (bosons), and 10 dimensions if there are both forces and matter (bosons and fermions) in the particle spectrum of the theory.
So where does gravity come in?
If the string traveling through spacetime is a closed string, then the spectrum of oscillations includes a particle with 2 units of spin and zero mass, with the right type of interactions to be the graviton, the particle that is the carrier of the gravitational force.
Where there are gravitons, then there must be gravity. Where is the gravity in string theory?
The classical theory of spacetime geometry that we call gravity consists of the Einstein equation, which relates the curvature of spacetime to the distribution of matter and energy in spacetime. But how do the Einstein equations come out of string theory?
If a closed string is traveling in a curved spacetime, then the coordinates of the string in spacetime feel this curvature as the string propagates. Once again, the answer lies on the string worldsheet. In order for their to be a consistent quantum theory in this case, the curved space in which the string travels must be a solution to the Einstein equations.

For anyone  interested the site is called the official string theory website.. So the macroscopic general relativity equations are necessary in order to have quantized strings

Now this is really something! This was a very convincing result for string theorists. Not only does string theory predict the graviton from flat spacetime physics alone, but string theory also predicts the Einstein equation will be obeyed by a curved spacetime in which strings propagate.

Italics mine
A: In general relativity 'gravity' is caused by following geodesics through curved space, so it is a pseudo force similar to the Coriolis or centrifugal forces.
In quantum gravity, gravitons mediate the interaction between masses the same way gluon's mediate the strong force, etc. So in quantum theories, gravity is similar to other fundamental forces.
