  We discuss structural aspects of the functional renormalisation group. Flows
for a general class of correlation functions are derived, and it is shown how
symmetry relations of the underlying theory are lifted to the regularised
theory. A simple equation for the flow of these relations is provided. The
setting includes general flows in the presence of composite operators and their
relation to standard flows, an important example being NPI quantities. We
discuss optimisation and derive a functional optimisation criterion.
Applications deal with the interrelation between functional flows and the
quantum equations of motion, general Dyson-Schwinger equations. We discuss the
combined use of these functional equations as well as outlining the
construction of practical renormalisation schemes, also valid in the presence
of composite operators. Furthermore, the formalism is used to derive various
representations of modified symmetry relations in gauge theories, as well as to
discuss gauge-invariant flows. We close with the construction and analysis of
truncation schemes in view of practical optimisation.
