Over the past decade, Carroll symmetry has sparked high interest due to its role in proposals for flat holography. In particular, one infinite-dimensional conformal extension of the Carroll algebra has been shown to be isomorphic to the BMS algebra in one higher dimension, while limiting arguments from the AdS/CFT correspondence have supported the idea that non-relativistic symmetries play a key role in holography for asymptotically flat spacetimes. In this talk, I will discuss the realisation of all infinite-dimensional conformal Carroll algebras, which include anisotropic scale transformations, as asymptotic symmetries at the conformal boundary of plane wave spacetimes. These simple yet highly symmetric spacetimes, which represent the generic geometries in the vicinity of null geodesics, are known to be connected to Carroll symmetries, photon ring physics, and the BMN limit of AdS/CFT. I will show that a one-parameter family of plane waves, encompassing flat spacetime as a special case, reproduces all conformal Carroll algebras in an asymptotic region that can be identified as the conformal boundary of these spacetimes. This result suggests a possible holographic description of gravity in plane wave backgrounds in terms of anisotropic conformal Carroll field theories. Time permitting, I will also comment on correlation functions in spatial conformal Carroll field theories.