  One of the most well known random fractals is the so-called Fractal
percolation set. This is defined as follows: we divide the unique cube in
$\mathbb{R}^d$ into $M^d$ congruent sub-cubes. For each of these cubes a
certain retention probability is assigned with which we retain the cube. The
interior of the discarded cubes contain no points from the Fractal percolation
set. In the retained ones we repeat the process ad infinitum. The set that
remains after infinitely many steps is the Fractal percolation set. The
homogeneous case is when all of these probabilities are the same. Recently,
there have been considerable developments in regards with the projection and
slicing properties in the homogeneous case. In the first part of this note we
give an account of some of these recent results and then we discuss the
difficulties and provide some new partial results in the non-homogeneous case.
