  Using the blackfold approach, we study new classes of higher-dimensional
rotating black holes with electric charges and string dipoles, in theories of
gravity coupled to a 2-form or 3-form field strength and to a dilaton with
arbitrary coupling. The method allows to describe not only black holes with
large angular momenta, but also other regimes that include charged black holes
near extremality with slow rotation. We construct explicit examples of electric
rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory,
with horizons of spherical and non-spherical topology. We also find new
families of solutions with string dipoles, including a new class of prolate
black rings. Whenever there are exact solutions that we can compare to, their
properties in the appropriate regime are reproduced precisely by our solutions.
The analysis of blackfolds with string charges requires the formulation of the
dynamics of anisotropic fluids with conserved string-number currents, which is
new, and is carried out in detail for perfect fluids. Finally, our results
indicate new instabilities of near-extremal, slowly rotating charged black
holes, and motivate conjectures about topological constraints on dipole hair.
