  In this article, we provide a review of the current state of the research of
the black hole shadow, focusing on analytical (as opposed to numerical and
observational) studies. We start with particular attention to the definition of
the shadow and its relation to the often used concepts of escape cone, critical
impact parameter and particle cross-section. For methodological purposes, we
present the derivation of the angular size of the shadow for an arbitrary
spherically symmetric and static space-time, which allows one to calculate the
shadow for an observer at arbitrary distance from the center. Then we discuss
the calculation of the shadow of a Kerr black hole, for an observer anywhere
outside of the black hole. For observers at large distances we present and
compare two methods used in the literature. Special attention is given to
calculating the shadow in space-times which are not asymptotically flat.
Shadows of wormholes and other black-hole impostors are reviewed. Then we
discuss the calculation of the black hole shadow in an expanding universe as
seen by a comoving observer. The influence of a plasma on the shadow of a black
hole is also considered.
