We compute the isospin asymmetries in B → (K * , ρ)γ and B → (K, K * , ρ)l + l − for low lepton pair invariant mass q 2 , within the Standard Model (SM) and beyond the SM (BSM) in a generic dimension six operator basis. Within the SM the CPaveraged isospin asymmetries for B → (K, K * , ρ)ll, between 1 GeV 2 ≤ q 2 ≤ 4m 2 c , are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-CP averaged asymmetries for B → ρll deviate by ≈ ±5% from the CP-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large q 2 (towards the endpoint). Two types of isospin violating effects are computed: ultraviolet (UV) isospin violation due to differences between operators coupling to up and down quarks, and infrared (IR) isospin violation where a photon is emitted from the spectator quark and is hence proportional to the difference between the up-and down-quark charges. These isospin violating processes may be subdivided into weak annihilation (WA), quark loop spectator scattering (QLSS) and a chromomagnetic contribution. Furthermore we discuss generic selection rules based on parity and angular momentum for the B → Kll transition as well as specific selection rules valid for WA at leading order in the strong coupling constant. We clarify that the relation between the K and the longitudinal part of the K * only holds for leading twist and for left-handed currents. In general the B → ρll and B → K * ll isospin asymmetries are structurally different yet the closeness of α CKM to ninety degrees allows us to construct a (quasi) null test for the SM out of the respective isospin symmetries. We provide and discuss an update on B(B 0 → K * 0 γ)/B(B s → φγ) which is sensitive to WA.