  We investigate the gravitational lensing by spinning Proca stars and the
shadows and lensing by Kerr black holes (BHs) with synchronised Proca hair,
discussing both theoretical aspects and observational constraints from the
Event Horizon Telescope (EHT) M87* and Sgr A* data. On the theoretical side,
this family of BHs interpolates between Kerr-like solutions -- exhibiting a
similar optical appearance to that of Kerr BHs -- to very non-Kerr like
solutions, exhibiting exotic features such as cuspy shadows, egg-like shadows
and ghost shadows. We interpret these features in terms of the structure of the
fundamental photon orbits, for which different branches exist, containing both
stable and unstable orbits, with some of the latter not being shadow related.
On the observational side, we show that current EHT constraints are compatible
with all such BHs that could form from the growth of the superradiant
instability of Kerr BHs. Unexpectedly, given the (roughly) 10% error bars in
the EHT data -- and in contrast to their scalar cousin model --, some of the
BHs with up to 40% of their energy in their Proca hair are compatible with the
current data. We estimate the necessary resolution of future observations to
better constrain this model.
