  During the last decade the Subspace Theorem found several quite unexpected
applications, mainly in the Diophantine Analysis and in the Transcendence
Theory. Among the great variety of spectacular results, I have chosen several
which are technically simpler and which allow one to appreciate how
miraculously does the Subspace Theorem emerge in numerous situations, implying
beautiful solutions to difficult problems hardly anybody hoped to solve so
easily. The three main topics discussed in this article are: the work of
Adamczewski and Bugeaud on complexity of algebraic numbers; the work of Corvaja
and Zannier on Diophantine equations with power sums; the work of Corvaja and
Zannier on integral points on curves and surfaces, and the subsequent
development due to Levin and Autissier. In particular, we give a complete proof
of the beautiful theorem of Levin and Autissier: an affine surface with 4 (or
more) properly intersecting ample divisors at infinity cannot have a Zariski
dense set of integral points.
