  In this survey we give an overview of recent developments on the Quantitative
Subspace Theorem. In particular, we discuss a new upper bound for the number of
subspaces containing the "large" solutions, obtained jointly with Roberto
Ferretti, and sketch the proof of the latter. Further, we prove a new gap
principle to handle the "small" solutions in the system of inequalities
considered in the Subspace Theorem. Finally, we go into the refinement of the
Subspace Theorem by Faltings and Wuestholz, which states that the system of
inequalities considered has only finitely many solutions outside some
effectively determinable proper linear subspace of the ambient solution space.
Estimating the number of these solutions is still an open problem. We give some
motivation that this problem is very hard.
