Primordial Black Holes (PBH) can be generated during inflation and account for the Dark Matter in the Universe. I will show that in all inflationary models constructed so far the gaussian approximation, so far used to estimate the PBH abundances, fails. I will revisit how a peak in the primordial power spectrum, responsable for the PBHs, can be generated and calculate the shape and amplitude of the non-gaussianities associated to this peak. These non gaussianities are typically of order one and spoils the gaussian predictions. I will finally comment on which models could possible be reliable by the sole use of the gaussian statistics.