  Black hole mimickers are possible alternatives to black holes, they would
look observationally almost like black holes but would have no horizon. The
properties in the near-horizon region where gravity is strong can be quite
different for both type of objects, but at infinity it could be difficult to
discern black holes from their mimickers. To disentangle this possible
confusion, we examine the near-horizon properties, and their connection with
far away properties, of some candidates to black mimickers. We study
spherically symmetric uncharged or charged but non-extremal objects, as well as
spherically symmetric charged extremal objects. Within the uncharged or charged
but non-extremal black hole mimickers, we study non-extremal
$\epsilon$-wormholes on the threshold of the formation of an event horizon, of
which a subclass are called black foils, and gravastars. Within the charged
extremal black hole mimickers we study extremal $\epsilon$-wormholes on the
threshold of the formation of an event horizon, quasi-black holes, and
wormholes on the basis of quasi-black holes from Bonnor stars. We elucidate,
whether or not the objects belonging to these two classes remain regular in the
near-horizon limit. The requirement of full regularity, i.e., finite curvature
and absence of naked behavior, up to an arbitrary neighborhood of the
gravitational radius of the object enables one to rule out potential mimickers
in most of the cases. A list ranking the best mimickers up to the worse is
given. Since, in observational astrophysics it is difficult to find extremal
configurations (the best mimickers in the ranking), whereas non-extremal
configurations are really bad mimickers, the task of distinguishing black holes
from their mimickers seems to be less difficult than one could think of.
