  Lovelock theory provides a tractable model of higher-curvature gravity in
which several questions can be studied analytically. This is the reason why, in
the last years, this theory has become the favorite arena to study the effects
of higher-curvature terms in the context of AdS/CFT correspondence. Lovelock
theory also admits extensions that permit to accommodate matter coupled to
gravity in a non-minimal way. In this setup, problems such as the backreaction
of matter on the black hole geometry can also be solved exactly. In this paper,
we study the thermodynamics of black holes in theories of gravity of this type,
which include both higher-curvature terms, U(1) gauge fields, and conformal
couplings with matter fields in D dimensions. These charged black hole
solutions exhibit a backreacting scalar field configuration that is regular
everywhere outside and on the horizon, and may exist both in asymptotically
flat and asymptotically Anti-de Sitter (AdS) spaces. We work out explicitly the
boundary action for this theory, which renders the variational problem
well-posed and suffices to regularize the Euclidean action in AdS. We also
discuss several interrelated properties of the theory, such as its duality
symmetry under field redefinition and how it acts on black holes and
gravitational wave solutions.
