We perform a comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b → sμ + μ - transition. We examine the effects of new vector-axial vector (VA), scalar-pseudoscalar (SP) " and tensor (T) interactions on the differential branching ratios and forward-backward asymmetries (A FB 's) of B o s → μ + μ - , B o d X s + μ - , B o s → μ + μ - γ, B o d → Kμ + μ - , and B o d → K*μ + μ - , taking the new-physics couplings to be real. In B o d → K*μ + μ - , we further explore the polarization fraction f L , the angular asymmetry A (2) T , and the longitudinaltransverse asymmetry A LT . We identify the Lorentz structures that would significantly impact these observables, providing analytical arguments in terms of the contributions from the individual operators and their interference terms. In particular, we show that while the new VA operators can significantly enhance most of the asymmetries beyond the Standard Model predictions, the SP and T operators can do this only for A FB in B o d → Kμ + μ - . © SISSA 2011.