On May 3, 2007 YouTube launched it's Partner Program. http://youtube-global.blogspot.com/2007/05/youtube-elevates-most-popular-users-to.html
At first about 40 people were in this program. Names such as SMPfilms, Renetto, LisaNova, Zipster08, HappySlip, Smosh, Lonelygirl15, and others. During this time you had to do an interview with them over the phone as they laid down the rules. It was made very clear what people could and could not monetize. Learn how it all started with Zipster08
At this time there was no way to apply, it was by invite only. Although Nalts found a way by launching a campaign to rally his subscribers
Each time you applied it took a few months to hear back from YouTube, due to the flood of applications. If you were turned down you were not able to re-apply for 60 days. I finally got in after my 3rd attempt on September 23, 2008. I was not able to successfully partner my other smaller channels until I grew them to decent size and I got them in finally in 2011.
In 2011 the Individual Partnership Program was rolled into the account monetization program. Basically this meant that you could place ads on your videos but did not have the full benefits of Partnership. This was considered a stepping stone for Partnership.
In the old Partner Program, IVP program, and Account Monetization program you had to fill out a claim form each time your video was reviewed. Newly approved YouTubers often had to wait days for their videos to be manually approved. Once YouTube got the chance they could trust you, and you had no copyright or TOS issues they allowed an automated system to approve your ads. A few times as a gag I even wrote, "I like turtles" on my claim form and it went through. Here is a video from my friend BionicDance giving a demo of what the old claim form looked like.
On April 12, 2012 YouTube rolled those in the account Monetization Program into the Partner Program without any notice. This caused quite a head ache in the forums as many people such as myself were left in the dark. YouTube finally pushed out this statement. http://youtubecreator.blogspot.com/2012/04/being-youtube-creator-just-got-even.html?showComment=1334275036850#c6300833837777462853
According to a live broadcast from YouTube Partner Support they do intend to roll out custom thumbnails, banners, scheduled publishing to all partners in good standing. However, they will not be expanding Livestreaming anymore. From now on they will be pushing the desolate wasteland known as Google Plus and their Hangouts On Air.
Just for the lulz please check out this example of YouTube's LiveStream and see how the quality is so much better than Google Hangouts on Air.
The Livestream was done in February 2011 when the technology was brand new while the previous video is Google's pride and joy and was made yesterday.
No wonder everyone refers to Google Plus as a ghost town.
Partner Support by email is pretty much dead now. Your best bet is to go to the help forums where people like myself try and answer your questions.
In my opinion YouTube's monetization is now mostly automated. I am basing this on what I am finding in the Help Forums. The old revenue sharing claim form has been replaced with a check box. Hundreds of thousands of new partners were added over night. That is simply too much for human review. My guess is they use a crawling program to skim through the video looking for content ID matches or otherwise copyrighted content as well as dangerous or sexual acts. They use a similar program to review flagged videos.