I am going to show our latest results (with Karoly Simon) about projections of Mandelbrot percolations (and also more general random sets). We show that under some condition (in case of Mandelbrot percolations equivalent to the expected dimension of the random set being greater than 1) for almost all realisations of the random set all its linear projections (ortogonal projections onto any line) and all its radial projections (radial projections onto any circle) contain an interval/arc. I will also mention the consequences of this result for the visibility of the random set (recent results of Jyvaskyla group).