  We determine the next-to-leading order renormalization group equations for
the Two-Higgs-Doublet model with a softly broken $Z_2$ symmetry and CP
conservation in the scalar potential. We use them to identify the parameter
regions which are stable up to the Planck scale and find that in this case the
quartic couplings of the Higgs potential cannot be larger than 1 in magnitude
and that the absolute values of the S-matrix eigenvalues cannot exceed 2.5 at
the electroweak symmetry breaking scale. Interpreting the 125 GeV resonance as
the light CP-even Higgs eigenstate, we combine stability constraints,
electroweak precision and flavour observables with the latest ATLAS and CMS
data on Higgs signal strengths and heavy Higgs searches in global parameter
fits to all four types of $Z_2$ symmetry. We quantify the maximal deviations
from the alignment limit and find that in type II and Y the mass of the heavy
CP-even (CP-odd) scalar cannot be smaller than 340 GeV (360 GeV). Also, we
pinpoint the physical parameter regions compatible with a stable scalar
potential up to the Planck scale. Motivated by the question how natural a Higgs
mass of 125 GeV can be in the context of a Two-Higgs-Doublet model, we also
address the hierarchy problem and find that the Two-Higgs-Doublet model does
not offer a perturbative solution to it beyond 5 TeV.
