  A vast literature on the theory and phenomenology of Two-Higgs-Doublet models
(2HDM) exists since long. However, the present situation demands a revisit of
some 2HDM properties. Now that a 125 GeV scalar resonance has been discovered
at the LHC, with its couplings to other particles showing increasing affinity
to the Standard Model Higgs-like behavior, the 2HDM parameter space is more
squeezed than ever. We briefly review the different parametrizations of the
2HDM potential and discuss the constraints on the parameter space arising from
the unitarity and stability of the potential together with constraints from the
oblique electroweak $T$-parameter. We also differentiate the consequences of
imposing a global continuous U(1) symmetry on the potential from a discrete
$Z_2$ symmetry.
