  Heavy meson decays provide an important platform for studies of both QCD and
electroweak dynamics, which may contain some portals to understanding of
nonperturbative QCD and physics beyond the Standard Model. The
factorization-assisted topological-amplitude approach was proposed to study
two-body non-leptonic $D$ meson decays, where a promising QCD inspired approach
from first principles is still missing. It was also applied to $B$ meson decays
whose subleading power contributions are difficult to calculate. By factorizing
topological amplitudes into short distance Wilson coefficients and long
distance hadronic matrix elements either to be calculated or to be
parameterized, it provides an effective framework to extract information of
nonperturbative dynamics involved. With important flavor SU(3) breaking effects
taken into account, the data of the decay branching ratios (and also CP
asymmetries in $B$ decays) can be fitted well. The extracted amplitudes were
further applied to make predictions for other observables, such as CP
asymmetries in $D$ decays, mixing parameters in the $D^0-\bar{D}^0$ system, and
so on. By this review, we will describe the formulation of the
factorization-assisted topological-amplitude approach and summarize its
applications in $D$ and $B$ meson decays and highlight some of its
achievements.
