  This article reviews recent inverse statistical-mechanical methodologies that
we have devised to optimize interaction potentials in soft matter systems that
correspond to stable "target" structures. We are interested in finding the
interaction potential, not necessarily pairwise additive or spherically
symmetric, that stabilizes a targeted many-body system by generally
incorporating complete configurational information. Unlike previous work, our
primary interest is in the possible many-body structures that may be generated,
some of which may include interesting but known structures, while others may
represent entirely new structural motifs. Soft matter systems, such as colloids
and polymers, offer a versatile means of realizing the optimized interactions.
It is shown that these inverse approaches hold great promise for controlling
self-assembly to a degree that surpasses the less-than-optimal path that nature
has provided. Indeed, we envision being able to "tailor" potentials that
produce varying degrees of disorder, thus extending the traditional idea of
self-assembly to incorporate both amorphous and crystalline structures as well
as quasicrystals. The notion of tailoring potentials that correspond to
targeted structures is motivated by the rich fundamental statistical-mechanical
issues and questions offered by this fascinating inverse problem as well as our
recent ability to identify structures that have optimal bulk properties or
desirable performance characteristics. Recent results have already led to a
deeper basic understanding of the mathematical relationship between the
collective structural behavior of many-body systems and their interactions, as
well as optimized potentials that enable self-assembly of ordered and
disordered particle configurations with novel structural and bulk properties.
