A number of the massive clusters in the halo, bulge, and disc of the Galaxy are not genuine globular clusters (GCs) but instead are different beasts altogether. They are the remnant nuclear star clusters (NSCs) of ancient galaxies since accreted by the Milky Way. While some clusters are readily identifiable as NSCs and can be readily traced back to their host galaxy (e.g. M54 and the Sagittarius Dwarf galaxy), others have proven more elusive. Here, we combine a number of independent constraints, focusing on their internal abundances and overall kinematics, to find NSCs accreted by the Galaxy and trace them to their accretion event. We find that the true NSCs accreted by the Galaxy are: M54 from the Sagittarius Dwarf,. Centari from Gaia-Enceladus/Sausage, NGC 6273 from Kraken, and (potentially) NGC 6934 from the Helmi Streams. These NSCs are prime candidates for searches of intermediate-mass black holes (BHs) within star clusters, given the common occurrence of galaxies hosting both NSCs and central massive BHs. No NSC appears to be associated with Sequoia or other minor accretion events. Other claimed NSCs are shown not to be such. We also discuss the peculiar case of Terzan 5, which may represent a unique case of a cluster-cluster merger.