The material surrounding accreting supermassive black holes connects the active galactic nucleus (AGN) with its host galaxy and, besides being responsible for feeding the black hole, provides important information on the feedback that nuclear activity produces on the galaxy. In this review we summarize our current understanding of the close environment of accreting supermassive black holes obtained from studies of local AGN carried out in the infrared and X-ray band. The structure of this circumnuclear material is complex, clumpy and dynamical, and its covering factor depends on the accretion properties of the AGN. From the infrared point of view, this obscuring material is a transition zone between the broad- and narrow-line region, and at least in some galaxies, it consists of two structures: an equatorial disk/torus and a polar component. In the X-ray regime, the obscuration is produced by multiple absorbers on various spatial scales, mostly associated with the torus and the broad-line region. In the next decade the new generation of infrared and X-ray facilities will greatly contribute to our understanding of the structure and physical properties of nuclear obscuration in AGN.