  We present a recursion relation for the explicit construction of integrable
spin chain Hamiltonians with long-range interactions. Based on arbitrary
short-range (e.g. nearest-neighbor) integrable spin chains, it allows to
construct an infinite set of conserved long-range charges. We explain the
moduli space of deformation parameters by different classes of generating
operators. The rapidity map and dressing phase in the long-range Bethe
equations are a result of these deformations. The closed chain asymptotic Bethe
equations for long-range spin chains transforming under a generic symmetry
algebra are derived. Notably, our construction applies to generalizations of
standard nearest-neighbor chains such as alternating spin chains. We also
discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6
supersymmetric gauge theories. Finally, we present a map between long-range and
inhomogeneous spin chains delivering more insight into the structures of these
models as well as their limitations at wrapping order.
