  Three-body $B$ decays not only significantly broaden the study of $B$ meson
decay mechanisms, but also provide information of resonant particles. Because
of complicate dynamics, it is very hard for us to study the whole phase space
in a specific approach. In this review, we take $B\to K({\cal R}\to) K^+K^-$
decays as examples and show the application of the perturbative QCD (PQCD)
approach in studying the quasi-two-body $B$ decays, where two particles move
collinearly with large energy and the bachelor one recoils back. To describe
the dynamics of two collinear particles, the ($S$, $P$ and $D$)-wave functions
of kaon-pair with different waves are introduced. By keeping the transverse
momenta, all possible diagrams including the hard spectator diagrams and
annihilation ones can be calculated in PQCD approach. Most results are well
consistent with the current measurements from BaBar, Belle and LHCb
experiments. Moreover, under the narrow-width approximation we can extract the
branching fractions of the two-body decays involving the resonant states, and
also predict the branching fractions of the corresponding quasi-two-body decays
$B\to K(\cal{R}\to )\pi^+\pi^-$. All prediction are expected to be tested in
the ongoing LHCb and Belle-II experiments.
