Who exactly gives out IP addresses to companies?

The American Registry of Internet Numbers (ARIN) is the organization in the U.S. that manages IP address numbers for the U.S. and assigned territories. Because Internet addresses must be unique and because address space on the Internet is limited, there is a need for some organization to control and allocate address number blocks. IP number management was formerly a responsibility of the Internet Assigned Numbers Authority (IANA), which contracted with Network Solutions Inc. for the actual services. In December 1997, IANA turned this responsibility over to ARIN, which, along with Reseaux IP Europeens (RIPE) and Asia Pacific Network Information Center (APNIC), now manages the world's Internet address assignment and allocation. domain name management is still the separate responsibility of Network Solutions and a number of other registrars accredited by the Internet Corporation for Assigned Names and Numbers (ICANN).