  We describe the idea of studying quantum gravity by means of dynamical
triangulations and give examples of its implementation in 2, 3 and 4 space time
dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We
introduce the so-called moment description which allows us to find the complete
perturbative solution of the generic model both away from and in the continuum.
Furthermore we show how one can easily by means of the moment variables define
continuum times for the model so that its continuum partition function agrees
with the partition function of the Kontsevich model except for some
complications at genus zero. Finally we study the non perturbative definition
of 2D quantum gravity provided by stochastic stabilization, showing how well
known matrix model characteristica can be given a simple quantum mechanical
interpretation and how stochastic quantization seems to hint to us the
possibility of a strong coupling expansion of 2D quantum gravity. For $d=3$ and
$d=4$ we consider the numerical approach to dynamically triangulated gravity.
We present the results of simulating pure gravity as well as gravity
interacting with matter fields. For $d=4$ we describe in addition the effect of
adding to the Einstein Hilbert action a higher derivative term.
