There are different forums which have applied this model. For example, ICANN (Internet Corporation for Assigned Names and Numbers) is the first multistakeholder experiment  - but there is also IGF (Internet Government Forum) and the NETmundial conference.

Wikipedia fact: The ICANN multistakeholder model was developed based on the input and collaborative effort of the global Internet stakeholders in the White Paper, a detailed policy statement commissioned by the United States government, which led to the establishment of ICANN in 1998.

But let's see what ICANN is exactly & how is it structured
 
The Internet Corporation for Assigned Names and Numbers (ICANN) is a global multistakeholder, not-for-profit, private sector organization that manages Internet resources for the public benefit. It is best known for its role as technical coordinator of the Internet’s Domain Name System and for managing the numbering system for IP (Internet Protocol) addresses and protocol port.
 
ICANN has a Board of Directors and different Advisory Committees and Supporting Organizations all working on a voluntary basis. In other words, in these Advisory Committees and Supporting Organizations is where the different stakeholders (as described in the previous article) can join the global Internet discussions, contribute at a policy level, make their voices heard irrespective of background, location and affiliation. More information about the ICANN structure is available here (see page 4) and here.
 
Yep, ICANN is huge and complex, but one more fundamental thing to know is related to one of its departments - the IANA
 
The Internet Assigned Numbers Authority (IANA) is a department of ICANN responsible for coordinating protocol parameters, IP addresses, the generic domain names and the country code domain names (more on these issues in the following articles). IANA is one of the Internet's oldest institutions, its services being nowadays provided by ICANN.

However, a debate on the transition process of the IANA functions from ICANN to the global community has started about one year ago during ICANN's meeting in Singapore. To be more clear, ICANN is providing the technical services mentioned above under a contractual relationship with the US government. Therefore, this is the reason why there has been a lot of pressure from the global community (especially from other governments) to determine the US to step out of its oversight role over the IANA functions. Although, historically speaking, there were very few occasions when the US Government intervened in IANA related decisions, since the Internet is global and for everyone, why should ONE single actor have the power to control it and theoretically have the last say?

In this context, the NTIA (the National Telecommunications and Information Administration) announced on the 14th of March 2014 that it intends to transition the IANA functions to the global multistakeholder community provided that certain criteria are met. NTIA is the Executive Branch agency that advises the President on telecommunications and information policy.
 
Now, I know it's already a lot, but bare with me for one more important thing.

In order to understand the Internet Governance setting better, it's essential to understand how the ICANN side of Internet business works - almost everything follows down format his.  

Let’s dig deeper into the contractual relationships that take place in ICANN
 
In ICANN there are several contractual relationships taking place for operating and coordinating the technical resources of the Internet:
 
•    ICANN performs the IANA functions on behalf of the United States Government through a contract with NTIA. This contract has been subsequently renewed and the last version was signed in 2012.
 
•         ICANN has a contractual agreement with the registry of a general top level domain name (gTLD) which grants one particular registry the right to operate one particular gTLD. This contract is called the Registry Agreement (RA).
 
•        ICANN accredits domain name registrars via the Registrar Accreditation Agreement (RAA). One of the contractual obligations of the above mentioned Registries is to allow domain name registration in their gTLD only via accredited Registrars.
 
Apart from this, ICANN has close relationships with root servers (which are the authoritative name servers that serve the Domain Name System root zone) and Regional Internet Registries (RIR) which are regional ISP organizations. There are 5 regions and one of the RIRs is for example RIPE NCC. For a global structure of the Internet Registry System see this diagram.

I hope this was useful! Domain names, country codes, new gTLD program & how the Internet works coming up next :)