  The decays $B_d^0\rightarrow D_d^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$
probe the CP-violating mixing phases $\phi_d$ and $\phi_s$, respectively. The
theoretical uncertainty of the corresponding determinations is limited by
contributions from penguin topologies, which can be included with the help of
the $U$-spin symmetry of the strong interaction. We analyse the currently
available data for $B^0_{d,s}\rightarrow D_{d,s}^-D_{d,s}^+$ decays and those
with similar dynamics to constrain the involved non-perturbative parameters.
Using further information from semileptonic $B_d^0\rightarrow
D_d^-\ell^+\nu_{\ell}$ decays, we perform a test of the factorisation
approximation and take non-factorisable $SU(3)$-breaking corrections into
account. The branching ratios of the $B_d^0\rightarrow D_d^-D_d^+$,
$B_s^0\rightarrow D_s^-D_d^+$ and $B_s^0\rightarrow D_s^-D_s^+$,
$B_d^0\rightarrow D_d^-D_s^+$ decays show an interesting pattern which can be
accommodated through significantly enhanced exchange and penguin annihilation
topologies. This feature is also supported by data for the $B_s^0\rightarrow
D_d^-D_d^+$ channel. Moreover, there are indications of potentially enhanced
penguin contributions in the $B_d^0\rightarrow D_d^-D_d^+$ and
$B_s^0\rightarrow D_s^-D_s^+$ decays, which would make it mandatory to control
these effects in the future measurements of $\phi_d$ and $\phi_s$. We discuss
scenarios for high-precision measurements in the era of Belle II and the LHCb
upgrade.
