  Singular actions on C*-algebras are automorphic group actions on C*-algebras,
where the group need not be locally compact, or the action need not be strongly
continuous. We study the covariant representation theory of such actions. In
the usual case of strongly continuous actions of locally compact groups on
C*-algebras, this is done via crossed products, but this approach is not
available for singular C*-actions (this was our path in a previous paper). The
literature regarding covariant representations for singular actions is already
large and scattered, and in need of some consolidation. We collect in this
survey a range of results in this field, mostly known. We improve some proofs
and elucidate some interconnections. These include existence theorems by
Borchers and Halpern, Arveson spectra, the Borchers-Arveson theorem, standard
representations and Stinespring dilations as well as ground states, KMS states
and ergodic states and the spatial structure of their GNS representations.
