Surveys above 10 keV represent one of the the best resources to provide an unbiased census of the population of Active Galactic Nuclei (AGN). We present the results of 60months of observation of the hard X-ray sky with Swift/BAT. In this timeframe, BAT detected (in the 1555 keV band) 720 sources in an allsky survey of which 428 are associated with AGN, most of which are nearby. Our sample has negligible incompleteness and statistics a factor of ∼2 larger over similarly complete sets of AGN. Our sample contains (at least) 15 bona-fide Compton-thick AGN and 3 likely candidates. Compton-thick AGN represent a ∼5% of AGN samples detected above 15 keV. We use the BAT dataset to refine the determination of the LogNLogS of AGN which is extremely important, now that NuSTAR prepares for launch, towards assessing the AGN contribution to the cosmic X-ray background. We show that the LogNLogS of AGN selected above 10 keV is now established to a ∼10% precision. We derive the luminosity function of Compton-thick AGN and measure a space density of 7.9 4.1 −2.9 10−5Mpc−3 for objects with a de-absorbed luminosity larger than 21042 erg s−1. As the BAT AGN are all mostly local, they allow us to investigate the spatial distribution of AGN in the nearby Universe regardless of absorption. We find concentrations of AGN that coincide spatially with the largest congregations of matter in the local (≤85Mpc) Universe. There is some evidence that the fraction of Seyfert 2 objects is larger than average in the direction of these de Show Partial Abstract