The experimental study of rare B decays is an excellent way to search for physics beyond the Standard Model. For processes that are highly suppressed within the Standard Model, even very small New Physics amplitudes could have measurable effects. Decays proceeding through loop topologies at leading order are a particularly attractive tool because contributions from virtual new particles may alter the decay rate, CP asymmetry and other observable quantities, thus providing a probe of New Physics at high mass scales. In this seminar I will review recent results from studies of rare B decays with the BaBar experiment at the SLAC PEP-II B factory. The focus will be be on radiative and leptonic decays and how they can be used to constrain New Physics model parameters.