  The structural degrees of freedom of a material are the various distortions
most straightforwardly activated by external stimuli. A highly successful
design strategy in materials chemistry involves controlling these individual
distortions to produce useful functional responses. In a ferroelectric such as
lead titanate, for example, the key degree of freedom involves displacements of
Pb$^{2+}$; by coupling these together, the system interacts with electric
fields. An exciting development has been to exploit the interplay between
different distortions: $e.g.$ generating polarisation by combining different
polyhedral rotations. Thus, degrees of freedom act as geometric `elements' that
can be combined to engineer materials with interesting properties. Just as the
discovery of new elements diversified chemical space, identifying new types of
structural degrees of freedom is a key strategy for developing new functional
materials. In this context, molecular frameworks are a fertile source of
unanticipated distortion types, many of which have no parallel in conventional
solid-state chemistry. Framework materials are solids whose structures are
assembled from nodes and linkers to form scaffolding-like networks. These
structures usually contain cavities, which may host additional ions for charge
balance. In the well-established systems---such as lead titanate---these
components are all atomic, but in molecular frameworks, at least one ion is
molecular. Here, we survey the unconventional degrees of freedom introduced
through the replacement of atoms by molecules. Our motivation is to understand
the role these new distortions play in different materials properties. The
various degrees of freedom are summarised and described in the context of
experimental examples. We highlight a number of directions for future research,
which demonstrate the extraordinary possibilities for this nascent field.
