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Falco, which includes 40 species of falcons, is a genus in the family Falconidae. 

Falco, Falcon: Hawk, eagle (Late Latin).

1/ Amur falcon (Cắt Amur, Falco amurensis)
2/ Laggar falcon (Cắt Ấn Độ, Falco jugger), also known as the lugger falcon or jugger 
3/ Oriental hobby (Cắt bụng hung, Falco severus)
4/ Peregrine falcon (Cắt lớn, Falco peregrinus), also known simply as the peregrine
5/ Common kestrel (Falco tinnunculus), also known as the European kestrel, Eurasian kestrel, or Old World kestrel
6/ Merlin (Cắt lưng xám, Falco columbarius) 
7/ Eurasian hobby (Cắt Trung Quốc, Falco subbuteo) or just hobby

The falcons and caracaras are around 65 species of diurnal birds of prey that make up the family Falconidae (representing all extant species in the order Falconiformes). The family is divided into three subfamilies: Herpetotherinae, which includes the laughing falcon and forest falcons; Polyborinae, which includes the spot-winged falconet and the caracaras; and Falconinae, the falcons and kestrels (Falco) and falconets (Microhierax).

The typical falconets, Microhierax, are a bird of prey genus in the family Falconidae.

Falco: Hawk, eagle (Late Latin).
Microhierax Greek mikros small; hierax hawk.

1/ Collared falconet (Cắt nhỏ bụng hung, Microhierax caerulescens)
2/ Pied falconet (Cắt nhỏ bụng trắng, Microhierax melanoleucos) 

Neohierax is a bird genus native to Indochina, in the family Falconidae. The genus was formerly included in the genus Polihierax.

Falco, Falcon: Hawk, eagle (Late Latin).
Neo: From Ancient Greek νέος (néos, “new, young”).
hierax: Greek for hawk.

1/  White-rumped falcon (Cắt nhỏ họng trắng, Neohierax insignis, formerly Polihierax insignis), also known as white-rumped pygmy falcon, white-rumped falconet, Fielden's falconet,or Burmese pigmy falcon

Phylogenetic analyses of morphological characteristics found the white-rumped falcon to be basal to the Falco clade, but separate from the clade containing the pygmy falcon (or African pigmy falcon, Polihierax semitorquatus) and Microhierax (falconets or pigmy falcons).

Research in molecular genetics has also found that the white-rumped falcon is more closely related to the Falco falcons than it is to the pygmy falcon.