  Within the supertwistor approach, we analyse the superconformal structure of
4D N = 2 compactified harmonic/projective superspace. In the case of 5D
superconformal symmetry, we derive the superconformal Killing vectors and
related building blocks which emerge in the transformation laws of primary
superfields. Various off-shell superconformal multiplets are presented both in
5D harmonic and projective superspaces, including the so-called tropical
(vector) multiplet and polar (hyper)multiplet. Families of superconformal
actions are described both in the 5D harmonic and projective superspace
settings. We also present examples of 5D superconformal theories with gauged
central charge.
