  The Standard Model (SM)-like couplings of the observed Higgs boson impose
strong constraints on the structure of any extended Higgs sector. We consider
the theoretical properties and the phenomenological implications of a generic
two Higgs doublet model (2HDM). This model constitutes a simple and attractive
extension of the SM that is consistent with the observation of the SM-like
Higgs boson and precision electroweak observables, while providing a potential
new source of CP-violation. In this paper we focus on the so-called Higgs
alignment limit of the generic 2HDM, where the neutral scalar field~$H_1$, with
the tree-level couplings of the SM Higgs boson, is a mass eigenstate that is
aligned in field space with the direction of the Higgs vacuum expectation
value. The properties of the two other heavier neutral Higgs scalars, $H_2$ and
$H_3$, in the alignment limit of the 2HDM are also elucidated. It is shown that
the couplings of $H_2$ and $H_3$ in the alignment limit are tightly constrained
and correlated. For example, in the exact alignment limit at tree level, for
bosonic final states $\text{BR}(H_{2,3} \to W^+W^-, ZZ, H_1 Z) = 0$ and
$\text{BR}(H^\pm \to W^\pm H_1) = 0$, whereas for fermionic final states
$\Gamma(H_2 \to f\bar f)/\Gamma(H_3 \to f\bar f) \sim M_2/M_3$ (where
$M_\alpha$ is the mass of $H_\alpha$). In some cases, the results of the
alignment limit differ depending on whether or not alignment is achieved via
the decoupling of heavy scalar states. In particular, in the exact alignment
limit without decoupling $\text{BR}(H_{2,3}\to H_1 H_1)=0$, whereas these
branching ratios are nonzero in the decoupling regime. Observables that could
be used to test the alignment scenario at the LHC are defined and discussed.
The couplings of the Higgs bosons away from their exact alignment values are
determined to leading order, and some consequences are elucidated.
