A lot is known about the forward iterates of an analytic function
which is bounded by $1$ in modulus on the unit disk $\mathbb{D}$. The
Denjoy-Wolff Theorem describes their convergence properties and
several authors, from the 1880's to the 1980's, have provided
conjugations which yield very precise descriptions of the
dynamics. Backward-iteration sequences are of a different nature
because a point could have infinitely many preimages as well as
none. However, if we insist in choosing preimages that are at a
finite hyperbolic distance each time, we obtain sequences which
have many similarities with the forward-iteration sequences, and
which also reveal more information about the map itself. In this
note we try to present a complete study of backward-iteration
sequences with bounded hyperbolic steps for analytic self-maps of
the disk.