  We advocate lattice methods as the tool of choice to constructively define a
background-independent theory of Lorentzian quantum gravity and explore its
physical properties in the Planckian regime. The formulation that arguably has
most furthered our understanding of quantum gravity (and of various pitfalls
present in the nonperturbative sector) uses dynamical triangulations to
regularize the nonperturbative path integral over geometries. Its Lorentzian
version in terms of Causal Dynamical Triangulations (CDT) - in addition to
having a definite quantum signature on short scales - has been shown to
reproduce important features of the classical theory on large scales. This
article recaps the most important developments in CDT of the last few years for
the physically relevant case of four spacetime dimensions, and describes its
status quo at present.
