  We carry out an extensive study of the holographic aspects of any-dimensional
higher-derivative Einstein-Maxwell theories in a fully analytic and
non-perturbative fashion. We achieve this by introducing the $d$-dimensional
version of Electromagnetic Quasitopological gravities: higher-derivative
theories of gravity and electromagnetism that propagate no additional degrees
of freedom and that allow one to study charged black hole solutions
analytically. These theories contain non-minimal couplings, that in the
holographic context give rise to a modified $\langle JJ\rangle$ correlator as
well as to a general $\langle TJJ \rangle$ structure whose coefficients we
compute. We constrain the couplings of the theory by imposing CFT unitarity and
positivity of energy (which we show to be equivalent to causality in the bulk)
as well as positive-entropy bounds from the weak gravity conjecture. The
thermodynamic properties of the dual plasma at finite chemical potential are
studied in detail, and we find that exotic zeroth-order phase transitions may
appear, but that many of them are ruled out by the physical constraints. We
further compute the shear viscosity to entropy density ratio, and we show that
it can be taken to zero while respecting all the constraints, providing that
the chemical potential is large enough. We also obtain the charged R\'enyi
entropies and we observe that the chemical potential always increases the
amount of entanglement and that the usual properties of R\'enyi entropies are
preserved if the physical constraints are met. Finally, we compute the scaling
dimension and magnetic response of twist operators and we provide a holographic
derivation of the universal relations between the expansion of these quantities
and the coefficients of $\langle JJ\rangle$ and $\langle TJJ \rangle$.
