  Charmless three-body decays of B mesons is studied using a simple model based
on the framework of the factorization approach. Hadronic three-body decays
receive both resonant and nonresonant contributions. Dominant nonresonant
contributions to tree-dominated three-body decays arise from the $b\to u$ tree
transition which can be evaluated using heavy meson chiral perturbation theory
valid in the soft meson limit. For penguin-dominated decays, nonresonant
signals come mainly from the penguin amplitude governed by the matrix elements
of scalar densities $<M_1M_2|\bar q_1 q_2|0>$. We use the measurements of $\bar
B^0\to K_SK_SK_S$ to constrain the nonresonant component of $<K\bar K|\bar
ss|0>$. The intermediate vector meson contributions to three-body decays are
identified through the vector current, while the scalar meson resonances are
mainly associated with the scalar density. While the calculated direct CP
violation in $B^-\to K^+K^-K^-$ and $B^-\to \pi^+\pi^-\pi^-$ decays agrees well
with experiment in both magnitude and sign, the predicted CP asymmetries in
$B^-\to \pi^- K^+K^-$ and $B^-\to K^-\pi^+\pi^-$ are wrong in signs when
confronted with experiment. It has been conjectured recently that a possible
resolution to this CP puzzle may rely on final-state rescattering of
$\pi^+\pi^-$ and $K^+K^-$. Assuming a large strong phase associated with the
matrix element $<K\pi|\bar sq|0>$ arising from some sort of power corrections,
we fit it to the data of $K^-\pi^+\pi^-$ and find a correct sign for $\pi^-
K^+K^-$.
