  We present new results towards the construction of the most general black
hole solutions in four-dimensional Fayet-Iliopoulos gauged supergravities. In
these theories black holes can be asymptotically AdS and have arbitrary mass,
angular momentum, electric and magnetic charges and NUT charge. Furthermore, a
wide range of horizon topologies is allowed (compact and noncompact) and the
complex scalar fields have a nontrivial radial and angular profile. We
construct a large class of solutions in the simplest single scalar model with
prepotential $F = -i X^0 X^1$ and discuss their thermodynamics. Moreover,
various approaches and calculational tools for facing this problem with more
general prepotentials are presented.
