  In this paper, we investigate the $L^p$ bilinear quasimode estimates on
compact Riemannian manifolds. We obtain results in the full range $p\ge2$ on
all $n$-dimensional manifolds with $n\ge2$. This in particular implies the
$L^p$ bilinear eigenfunction estimates. We further show that all of these
estimates are sharp by constructing various quasimodes and eigenfunctions that
saturate our estimates.
