  Dimension theory lies at the heart of fractal geometry and concerns the
rigorous quantification of how large a subset of a metric space is. There are
many notions of dimension to consider, and part of the richness of the subject
is in understanding how these different notions fit together, as well as how
their subtle differences give rise to different behaviour. Here we survey a new
approach in dimension theory, which seeks to unify the study of individual
dimensions by viewing them as different facets of the same object. For example,
given two notions of dimension, one may be able to define a continuously
parameterised family of dimensions which interpolates between them. An
understanding of this `interpolation function' therefore contains more
information about a given object than the two dimensions considered in
isolation. We pay particular attention to two concrete examples of this, namely
the \emph{Assouad spectrum}, which interpolates between the box and
(quasi-)Assouad dimension, and the \emph{intermediate dimensions}, which
interpolate between the Hausdorff and box dimensions.

Metric Geometry;Classical Analysis and ODEs;Dynamical Systems