Probing New Physics in B Penguins

Constraints placed on physics beyond the Standard Model from the recent CLEO observation of the inclusive decay $B\to X_s\gamma$ are summarized. Further searches for new physics using the process $B\to X_s\ell^+\ell^-$ are discussed. {Presented at the {\it International Workshop on B Physics: Physics Beyond the Standard Model at the B Factory}, Nagoya, Japan, October 26-28, 1994}