After an extensive introduction to the asymptotic safety approach to quantum gravity, this thesis explains recent key advances
reported in four influential papers. Firstly, two exact solutions to the reconstruction problem (how to recover a bare action
from the effective average action) are provided. Secondly, the fundamental requirement of background independence in quantum
gravity is successfully implemented. Working within the derivative expansion of conformally reduced gravity, the notion of
compatibility is developed, uncovering the underlying reasons for background dependence generically forbidding fixed points
in such models. Thirdly, in order to understand the true nature of fixed-point solutions, one needs to study their asymptotic
behaviour. The author carefully explains how to find the asymptotic form of fixed point solutions within the f(R) approximation.
Finally, the key findings are summarised and useful extensions of the work are identified. The thesis finishes by considering
the need to incorporate matter into the formalism in a compatible way and touches upon potential opportunities to test asymptotic
safety in the future.