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We summarize recent results on the properties of near-horizon metrics indifferent spherically symmetric space-times, including Kantowski-Sachscosmological models whose evolution begins with a horizon (the so-called NullBig Bang) and static metrics related to black holes. We describe the types ofmatter compatible with cosmological and black-hole horizons. It turns out, inparticular, that a black hole horizon can be in equilibrium with a fluid ofdisordered cosmic strings ("black holes can have curly hair"). We also discussdifferent kinds of horizons from the viewpoint of the behavior of tidal forcesacting on an extended body and recently classified as "usual", "naked" and"truly naked" ones; in the latter case, tidal forces are infinite in a freelyfalling reference frame. It is shown that all truly naked horizons, as well asmany of those previously characterized as naked and even usual ones, do notadmit an extension and therefore must be considered as singularities. The wholeanalysis is performed locally (in a neighborhood of a candidate horizon) in amodel-independent manner. Finally, the possible importance of some of thesemodels in generating dynamic, perturbatively small vacuum fluctuationcontributions to the cosmological constant (within a cosmologicalCasimir-effect approach to this problem) is discussed.

Dark energy, exotic matter and properties of horizons in black hole physics and cosmology