Q:

How were Millennium Problems chosen? (according to what criteria)

I am making a presentation about Millennium Problems. There are 7 Millennium Problems but a lot of unsolved mathematics problems are also waiting to be solved. I know that these problems are much more important than many others but I need a more detailed explanation.  Why these 7? Who decided? Are they really the most important ones in mathematics? For example, one question comes to mind is why 3n+1 conjecture is not in this list, maybe solving it will provide us great mathematical devices like FLT. I will be really glad if you can provide some reliable links or a detailed explanation.
Thank you,
TT

A:

The website of the Clay Mathematical Institute writes the following:

The focus [...] was on important classic questions that have resisted solution for many years.

Arthur M. Jaffe, once director of the Clay Mathematical Insitute, wrote on the history of conceiving the Millennium Prize Problems (emphasis mine). 

As a first step, I requested that each SAB member submit a personal list of top questions. Each
  of these questions should be difficult and important — a  time-tested  challenge  on  which  mathematicians had worked without success. [...] We  added  questions to the list one by one. With each new question we asked whether the list should be expanded
  or whether it might be improved by substituting a
  new question. [...] While each problem on the list was central and
  important, I want to stress that the SAB did not envisage making a definitive list, nor even a representative set of famous unsolved problems.
  Rather, personal taste entered our choices; a different scientific advisory board undoubtedly would
  have come up with a different list. The persons we
  consulted were experts, but they were chosen under
  pressure of time. However, the spirit of the selection transcends these decisions: the resulting list
  represents an honest attempt to convey some excitement about mathematics. We do not wish to address the question, “Why is Problem A not on your
  list?” Rather we say that the list highlights seven
  historic, important, and difficult open questions in
  mathematics.

The source of the above article also describes in more detail the actual process of creating the final list of $7$ problems.
For reference, the seven problems are:

The Birch-Swinnerton-Dyer conjecture
  (Andrew Wiles)
The Hodge conjecture (Pierre Deligne)
The Navier-Stokes equation has
  smooth solutions (Charles Fefferman)
P is not NP (Stephen Cook)
The Poincaré conjecture (John Milnor)
Quantum Yang-Mills theory exists
  with a mass gap (Arthur Jaffe and Edward
  Witten)
The Riemann hypothesis (Enrico
  Bombieri)

