  Charmless 3-body decays of B mesons are studied in a simple model based on
the factorization approach. We have identified two distinct sources of
nonresonant contributions: a small contribution from the tree transition and a
large source of the nonresonant signal in the matrix elements of scalar
densities, e.g., $<K\bar K|\bar ss|0>$, induced from the penguin transition.
This explains the dominance of the nonresonant background in $B\to KKK$ decays,
the sizable nonresonant fraction in $K^-\pi^+\pi^-$ and $\bar K^0\pi^+\pi^-$
modes and the smallness of nonresonant rates in $B\to \pi\pi\pi$ decays. The
seemingly huge discrepancy between BaBar and Belle for the nonresonant
contribution in the decay $B^-\to K^-\pi^+\pi^-$ is now relieved. We have
computed the resonant and nonresonant contributions to charmless 3-body decays
and determined the rates for the quasi-two-body decays $B\to VP$ and $B\to SP$.
Time-dependent CP asymmetries $\sin2\beta_{\rm eff}$ and $A_{CP}$ in
$K^+K^-K_S,K_SK_SK_S,K_S\pi^+\pi^-$ and $K_S\pi^0\pi^0$ modes are estimated.
