Who controls IP assignments?

Seal

IANA controls assignment of IP addresses on the Internet. But IANA have passed assignment down to several registries. They are as follows:

AfriNIC (African Network Information Centre) - Africa Region
APNIC (Asia Pacific Network Information Centre) - Asia/Pacific Region
ARIN (American Registry for Internet Numbers) - North America Region
LACNIC (Regional Latin-American and Caribbean IP Address Registry) – Latin America and some Caribbean Islands
RIPE NCC (Réseaux IP Européens) - Europe, the Middle East, and Central Asia

Global assignments are found at http://www.iana.org/assignments/ipv4-address-space