  This paper gives a broad account of the various sequent-based proof
formalisms in the proof-theoretic literature. We consider formalisms for
various modal and tense logics, intuitionistic logic, conditional logics, and
bunched logics. After providing an overview of the logics and proof formalisms
under consideration, we show how these sequent-based formalisms can be placed
in a hierarchy in terms of the underlying data structure of the sequents. We
then discuss how this hierarchy can be traversed using translations.
Translating proofs up this hierarchy is found to be relatively easy while
translating proofs down the hierarchy is substantially more difficult. Finally,
we inspect the prevalent distinction in structural proof theory between
'internal calculi' and 'external calculi'. It is observed that these classes
resist a rigorous separation, and we critically assess the properties that
(calculi from) these classes are purported to possess.
