The taxon is represented by a single family, the Apterygidae, confined to New Zealand:

Genus-level classification of extant Apterygiformes. 

References

Burbridge ML, Colbourne RM, Robertson HA, and Baker AJ (2003), Molecular and other biological evidence supports the recognition of at least three species of brown kiwi, Conserv. Genet. 4, 167-177. (abstract)

de Cahsan B, and Westbury MV (2020), Complete mitochondrial genomes offer insights into the evolutionary relationships and comparative genetic diversity of New Zealand´s iconic kiwi (Apteryx spp.), New Zealand J. Zool. 47, 291-299. (pdf)

Shepherd LD, Worthy TH, Tennyson AJD, Scofield RP, Ramstad KM, and Lambert DM (2012), Ancient DNA analyses reveal contrasing phylogeographic patterns amongst kiwi (Apteryx spp.) and a recently extinct lineage of Spotted Kiwi, PLoS ONE 7, e:42384. (pdf)

Shepherd LD, Tennyson AJD, Robertson HA, Colbourne RM, and Ramstad KM (2021), Hybridisation in kiwi (Apteryx; Apterygidae) requires taxonomic revision for the Great Spotted Kiwi, Avian Res. 12, e:24. (free pdf)