In a similar way that a DNS server would be 'authoritative' for a domain zone (*.example.com), a DNS server will be in charge of resolving the reverse DNS zones: and instead of having A records you will have PTR records.
The process of reverse lookup is almost exactly the same as forward lookup but it uses the IP instead of the FQDN:
How a reverse DNS lookup is accomplished:
* The DNS resolver reverses the IP, and adds it to ".inaddr.arpa" (or ".ip6.arpa" for IPv6 lookups), turning 192.0.2.25 into 25.2.0.192.inaddr.arpa.
* The DNS resolver then looks up the PTR record for 25.2.0.192.inaddr.arpa.
- The DNS resolver asks the root servers for the PTR record for 25.2.0.192.inaddr.arpa.
- The root servers refer the DNS resolver to the DNS servers in charge of the Class A range (192.inaddr.arpa, which covers all IPs that begin with 192).
- In almost all cases, the root servers will refer the DNS resolver to a "RIR" ("Regional Internet Registry"). These are the organizations that allocate IPs. In general, ARIN handles North American IPs, APNIC handles AsianPacific IPs, and RIPE handles European IPs.
- The DNS resolver will ask the ARIN DNS servers for the PTR record for 25.2.0.192.inaddr.arpa.
- The ARIN DNS servers will refer the DNS resolver to the DNS servers of the organization that was originally given the IP range. These are usually the DNS servers of your ISP, or their bandwidth provider.
- The DNS resolver will ask the ISP's DNS servers for the PTR record for 25.2.0.192.inaddr.arpa.
- The ISP's DNS servers will refer the DNS resolver to the organization's DNS servers.
- The DNS resolver will ask the organization's DNS servers for the PTR record for 25.2.0.192.inaddr.arpa.
- The organization's DNS servers will respond with "host.example.com".
Reference:
http://www.dnsstuff.com/reverse-dns-faq/