I will review what we have learnt on absorption in the local Universe using a complete sample of AGN detected by Swift ​/​BAT. The fraction of Compton-thick AGN represents only 5% of the total AGN population detected by Swift ​/​BAT. Nonetheless, when the bias of BAT against the detection of the most absorbed sources is taken into account, I show that the intrinsic fraction of CT AGN is ~20%. With these data we investigated the possible correlation between the radio and the X-ray emission at the highest radio and X-ray frequencies. We found 37 AGN with a high probability of association (>80 per cent), among which 19 are local Seyfert galaxies (with median redshift z = 0.03) and 18 blazars. We found that ≈20 per cent of the AGN detected in hard X-rays are also bright radio sources at 20 GHz, but the apparent correlation between the radio and hard X-ray luminosity is completely driven by the different median redshifts of the two subgroups of AGN. When we ​focus on the local Seyfert sample we find no evidence of a correlation between their 20 GHz and 15?55 keV power. Therefore it appears that at high frequencies the radio?X connection, which had been previously observed at lower frequencies, disappears ​​.​ Intriguingly the same evidence emerges when X-ray luminosities are compared to VLBI data.​