Like Loop Quantum Gravity, causal dynamical triangulation (CDT) is a bottom-up, background independent, non-perturbative theory of Quantum gravity. Most theorists agree that near the Planck scale, the structure of space-time is in a constant state of change. This theory divides space-time into a series of building blocks called pentachorons. These are four dimensional analogues of triangles; a normal triangle is two dimensional, a 2-simplex, a tetrahedron is a three dimensional triangle, a 3-simplex having four sides, and the pentachoron is the equivalent in four dimensions, a 4-simplex. Each 4-simplex is connected to adjacent 4-simplexes. What is critical in CDT is that where edges that represent time join onto the next 4-simplex, the directions of time must align to maintain causality. There have been previous attempts to create theories based on this approach, but they lacked the requirement to maintain causality. One of the main tools used in this theory is a causal, non-perturbative version of Richard Feynman's path integral approach to analyzing Quantum behavior.
At cosmic scales, CDT produces the quasi-classical four dimensional space-time we observe. It also shows that the dimensionality of spacetime reduces smoothly to two dimensions at very short distances, around the Plank scale, indicating that spacetime geometry near the Planck scale behaves in a highly non-classical way. This behavior makes it a very attractive theoretical tool. Beyond this basic introduction, the methodology becomes highly mathematical, and as my understanding of Regge calculus is close to non-existant, this is as far as I go!
There is a very interesting lecture by Renate Loll, one of the originators of the theory, at the Loops'05 conference and a somewhat more technical letter by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz on the emergence of a 4D world from causal quantum gravity.
Causal Dynamical Triangulation