  Multi-black hole solutions play a relevant role both from the theoretical and
the phenomenological point of view. In this Thesis, we construct some regular
multi-black hole spacetimes in pure Einstein's General Relativity with the aid
of solution generating techniques. We begin with a perspective on the history
of solution generating techniques, and then we explain in detail the Ernst
formalism and the inverse scattering method. These are the techniques that are
applied in the rest of the Thesis. Subsequently, we construct multi-black hole
solutions embedded in an external gravitational field: it is possible to obtain
an equilibrium configuration in many interesting cases, like a collection of
collinear static black holes or a chain of accelerating black holes, by
choosing appropriately the multipole parameters of the field. Then, we consider
the expanding bubbles of nothing as a background for multi-black hole and black
ring solutions. The expanding behaviour of the bubbles provides the force
necessary to balance the gravitational attraction among the black holes, and
hence to reach the equilibrium. Finally, we construct a solution that
represents a black hole embedded in a "swirling" universe, which describes a
spacetime whirlpool. Moreover, we discuss the possibility of implementing the
swirling background in order to enforce the spin-spin configuration, and reach
an equilibrium configuration in a double-Kerr spacetime.
