Can a relativistic QFT be consistently described as a theory of localizable particles? There are many well-known obstructions with such a description. In this talk we will trace how such obstructions arise in the regime between non-relativistic quantum mechanics and relativistic QFT. Perhaps surprisingly, we find that the localizability issues persist in the non-relativistic regime of a relativistic QFT. We link this to the persistence of vacuum entanglement alluding to the Reeh-Schlieder theorem (arXiv:1902.10684v2). Finally, we will discuss how such considerations are becoming increasingly relevant for the relatively young field of Relativistic Quantum Information.