The term hawk refers to birds of prey in any of three senses:

Strictly, to mean any of the species in the genera Accipiter, Micronisus, Melierax, Urotriorchis, and Megatriorchis. The widespread Accipiter genus includes goshawks, sparrowhawks, the Sharp-shinned Hawk and others. They are mainly woodland birds that hunt by sudden dashes from a concealed perch. They usually have long tails and high visual acuity.
More generally, to mean small to medium-sized birds that are members of the Accipitridae, the family which includes the true hawks (Accipiters) and also eagles, kites, harriers, buzzards, and Old World vultures.
Loosely, to mean almost any bird of prey.
The common names of birds in various parts of the world often use hawk loosely. For example, in North America, the buzzards (Buteo) are often called "hawks".

The true hawks form the sub-family Accipitrinae and most are in the genus Accipiter.

In February 2005 the Canadian scientist Dr Louis Lefebvre announced a method of measuring avian IQ in terms of their innovation in feeding habits. Hawks were named among the most intelligent birds based on this scale.

Species
ORDER FALCONIFORMES
Family Accipitridae
Subfamily Elaninae
Subfamily Milvinae
Subfamily Accipitrinae
Genus Accipiter
Goshawk, A. gentilis
Sparrowhawk, A. nisus
Grey-bellied Goshawk, A. poliogaster
Crested Goshawk, A. trivirgatus
Sulawesi Goshawk, A. griseiceps
Red-chested Goshawk, A. toussenelii
African Goshawk, A. tachiro
Chinese Goshawk, A. soloensis
Frances' Goshawk, A. francesii
Spot-tailed Goshawk, A. trinotatus
Grey Goshawk, A. novaehollandiae
Brown Goshawk, A. fasciatus
Black-mantled Goshawk, A. melanochlamys
Pied Goshawk, A. albogularis
Fiji Goshawk, A. rufitorques
White-bellied Goshawk, A. haplochrous
Moluccan Goshawk, A. henicogrammus
Grey-headed Goshawk, A. poliocephalus
New Britain Goshawk, A. princeps
Black Goshawk, A. melanoleucus
Henst's Goshawk, A. henstii
Meyer's Goshawk, A. meyerianus
Chestnut-flanked Sparrowhawk, A. castanilius
Nicobar Sparrowhawk, A. butleri
Levant Sparrowhawk, A. brevipes
Slaty-mantled Sparrowhawk, A. luteoschistaceus
Imitator Sparrowhawk, A. imitator
Red-thighed Sparrowhawk, A. erythropus
Little Sparrowhawk, A. minullus
Japanese Sparrowhawk, A. gularis
Small Sparrowhawk, A. nanus
Rufous-necked Sparrowhawk, A. erythrauchen
Collared Sparrowhawk, A. cirrocephalus
New Britain Sparrowhawk, A. brachyurus
Vinous-breasted Sparrowhawk, A. rhodogaster
Madagascar Sparrowhawk, A. madagascariensis
Ovampo Sparrowhawk, A. ovampensis
Rufous-chested Sparrowhawk, A. rufiventris
Shikra, A. badius
Tiny Hawk, A. superciliosus
Semicollared Hawk, A. collaris
Sharp-shinned Hawk, A. striatus
White-breasted Hawk, A. chionogaster
Plain-breasted Hawk, A. ventralis
Rufous-thighed Hawk, A. erythronemius
Cooper's Hawk, A. cooperii
Gundlach's Hawk, A. gundlachi
Bicoloured Hawk, A. bicolor
Besra, A. virgatus
Genus Micronisus
Gabar Goshawk, M. gabar
Genus Melierax
Dark Chanting Goshawk, M. metabates
Eastern Chanting Goshawk, M. poliopterus
Pale Chanting Goshawk, M. canorus
Genus Urotriorchis
Long-tailed Hawk, U. macrourus
Genus Erythrotriorchis
Red Goshawk, E. radiatus
Chestnut-shouldered Goshawk, E. buergersi
Genus Megatriorchis
Doria's Goshawk, M. doriae
Subfamily Buteoninae
Subfamily Aegypiinae: Old World vultures
Subfamily Circinae: harriers
Subfamily Circaetinae: snake-eagles