  We study the effects of $\mathcal{CP}$-violating phases on the phenomenology
of the Higgs sector of the MSSM. Complex parameters in the MSSM lead to
$\mathcal{CP}$-violating mixing between the tree-level $\mathcal{CP}$-even and
$\mathcal{CP}$-odd neutral Higgs states, leading to three new loop-corrected
mass eigenstates $h_a$, $a \in \lbrace 1,2,3\rbrace$. For scenarios where a
light Higgs boson at about 125 GeV can be identified with the observed signal
and where the other Higgs states are significantly heavier, a large admixture
of the heavy neutral Higgs bosons occurs as a generic feature if
$\mathcal{CP}$-violating effects are taken into account. Including interference
contributions in the predictions for cross sections times branching ratios of
the Higgs bosons is essential in this case. As a first step, we present the
gluon-fusion and bottom-quark annihilation cross sections for $h_a$ for the
general case of arbitrary complex parameters, and we demonstrate that squark
effects strongly depend on the phases of the complex parameters. We then study
the effects of interference between $h_2$ and $h_3$ for the example of the
process $b\bar{b} \to \tau^+\tau^-$. We show that large destructive
interference effects modify LHC exclusion bounds such that parts of the
parameter space that would be excluded by MSSM Higgs searches under the
assumption of $\mathcal{CP}$-conservation open up when the possibility of
$\mathcal{CP}$-violation in the Higgs sector is accounted for.
