  The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation
(DP1). Solutions of DP1 are classified under criterion of their behavior while
argument tends to infinity. The Isomonodromic Deformations Method yields
asymptotic formulae for regular solutions of DP1. DP1 is an integrable system,
what allows to develop appropriate Whitham theory. Asymptotics of singular
solutions of DP1 are calculated by using the Whitham method.
