This order is represented by a single family, Falconidae (falcons, carcaras). 

Genus-level timetree of extant Falconidae based on Fuchs et al. (2015) and Oswald et al. (2019), with the distribution of each taxon being indicated by the colour-code used throughout this website (Distribution code). The divergence times of subfamilies follow Kuhl et al. (2021), with adjustments from Stiller et al. (2024).

Species-level classification of extant Falconidae after Fuchs et al. (2015). 

References

Fuchs J, Johnson JA, and Mindell DP (2012), Molecular systematics of the caracaras and allies (Falconidae: Polyborinae) inferred from mitochondrial and nuclear sequence data, Ibis 154, 520-532. (abstract)

Fuchs J, Johnson JA, and Mindell DP (2015), Rapid diversification of falcons (Aves: Falconidae) due to expansion of open habitats in the Late Miocene, Mol. Phylogenet. Evol. 82, 166-182. (abstract)

Kuhl H, Frankl-Vilches C, Bakker A, Mayr G, Nikolaus G, Boerno ST, Klages S, Timmermann B, and Gahr M (2021), An unbiased molecular approach using 3'UTRs resolves the avian family-level tree of life, Mol. Biol. Evol. 38 (1), 108-127. (pdf)

Mindell DP, Fuchs J, and Johnson JA (2018), Phylogeny, taxonomy, and geographic diversity of diurnal raptors: Falconiformes, Accipitriformes, and Cathartiformes, In: Sarasola, J.H. et al., Birds of prey, Chapter 1, 3-32. Springer.  (abstract)

Oswald JA, Allen JM, Witt KE, Folk RA, Albury NA, Steadman DW, and Guralnick RP (2019), Ancient DNA from a 2,500-year-old Caribbean fossil places an extinct bird (Caracara creightoni) in a phylogenetic context, Mol. Phylogenet. Evol. 140:106576. (abstract)