  In recent years, there has been much progress in the field of structural
Ramsey theory, in particular in the study of big Ramsey degrees. In all known
examples of infinite structures with finite big Ramsey degrees, there is in
fact a single expansion of the structure, called a big Ramsey structure, which
correctly encodes the exact big Ramsey degrees of every finite substructure
simultaneously. The first half of the article collects facts about this
phenomenon that have appeared in the literature into a single cohesive
framework, thus offering a conceptual survey of big Ramsey structures. We
present some original results indicating that the standard methods of proving
finite big Ramsey degrees automatically yield big Ramsey structures, often with
desirable extra properties. The second half of the article is a survey in the
more traditional sense, discussing numerous examples from the literature and
showing how they fit into our framework. We also present some general results
on how big Ramsey degrees are affected by expanding structures with unary
functions.
