  We study clustering and percolation phenomena in the Vicsek model, taken here
in its capacity of prototypical model for dry aligning active matter. Our
results show that the order-disorder transition is not related in any way to a
percolation transition, contrary to some earlier claims. We study geometric
percolation in each of the phases at play, but we mostly focus on the ordered
Toner-Tu phase, where we find that the long-range correlations of density
fluctuations give rise to a novel anisotropic percolation transition.
