  We compute the isospin asymmetries in $B \to (K^*,\rho) \gamma$ and $B\to
(K,K^*,\rho) l^+l^-$ 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 CP-averaged isospin asymmetries for $B \to
(K,K^*,\rho) ll$, between $1{\rm GeV}^2 \leq q^2 \leq 4m_c^2$, are predicted to
be small (below 1.5%) though with significant cancellation. In the SM the
non-CP averaged asymmetries for $B \to \rho ll$ deviate by $\approx \pm 5%$
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 $B \to Kll$ 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 $B \to \rho ll$ and $B \to K^*ll$ isospin asymmetries are
structurally different yet the closeness of $\alpha_{\rm CKM}$ to ninety
degrees allows us to construct a (quasi) null test for the SM out of the
respective isospin symmetries. We provide an update on ${\cal B}(B^0 \to
K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ which is sensitive to WA.
