Abstract: Random geometry is of growing interest both to mathematicians and physicists. Its development may follow the same pattern than the one of ordinary geometry, from lower dimensional objects such as curves and surfaces embedded in a flat vector space to higher dimensional objects independent of any background. Mathematical progress in this direction is welcome by physicists working on the long term challenge of quantizing gravity. We shall in particular describe recently introduced random tensor models whose Feynman amplitudes ponder discretized geometries with their natural Einstein-Hilbert weight.