Penguin $B$ Decays $b\rightarrow s l^+l^-$ and $b\rightarrow s g$

The penguin mediated processes $b\rightarrow s g$ and $b\rightarrow s l^+l^-$ are studied. In the Standard Model, for the leptonic modes improvement in experimental limits will put strigient bounds on the top mass, where the present limit from $b\rightarrow s \mu^+\mu^-$ is 390 GeV. For hadronic penguin processes, although the gluonic penguin dominates, we find the electroweak contribution are around 30\% for the upper range allowed top mass. The branching ratio for $B\rightarrow X_s \phi$ is predicted to be in the range $(0.6\sim 2)\times 10^{-4}$. Effects of the charged Higgs in two Higgs doublet models are discussed.