It's helped to have the greatest quarterback of all-time. Not needing to ever replace your quarterback is the biggest deal in football. Only the Steelers have really had a comparable run where they had two distinct teams win Super Bowls with the quarterback remaining the same. Maybe the Ravens, who had similar reloads, though there it was Ray Lewis as the continuous piece. Neither the Steelers nor the Ravens have seen the breadth nor depth of success that the Patriots have, however, and this 'third' Steelers era of the 2000s has been noticeably less successful than the two previous.
I might date those as follows, with the defining players of each range of years...
First period, 2001-2005: This period is defined by players like Adam Vinatieri, Deion Branch, Troy Brown, David Patten, Richard Seymour, Antowain Smith, Corey Dillon, Mike Vrabel, Kevin Faulk, Ty Law, Rodney Harrison, and Tedy Bruschi. It's marked by a dominant defense, with Tom Brady growing into his role as a franchise QB. The first period ends with the playoff loss to Denver and the departure of Deion Branch and Adam Vinatieri following the 2005 season.
Second period, 2006-2010: This period is defined by the acquisitions of Randy Moss and Wes Welker prior to the 2007 season, and those players are its most iconic. Faulk and Seymour remained as holdovers from the previous era, while new players and stars like Laurence Maroney, Asante Samuel, Jerod Mayo, Logan Mankins, Ty Warren, Stephen Gostkowski, and Vince Wilfork emerged. Beginning in 2006, Brady emerged as a true superstar, a quarterback who would set records and who put any question that he was a system QB with a good defense to bed. This period ends with the departure of Randy Moss.
Third period, 2010-2017: This period is defined most notably by the emergence of Rob Gronkowski as the greatest tight end of all-time following the departure of Moss and eventually Welker. Other defining players include Aaron Hernandez (for good or ill), Dion Lewis, Danny Woodhead, Rob Ninkovich, Julian Edelman, Danny Amendola, Nate Solder, Donta Hightower, Malcolm Butler, Matt Slater, and Devin McCourty, as well as Gostkowski. This period cements Brady as the greatest quarterback of all-time. This era ends with the Super Bowl loss to the Eagles, the departure of Lewis, Butler, Amendola, and Solder, and the diminishing effectiveness of Gronk.
Fourth period, 2018-present: The history of this period has yet to be written, but it's likely to be the last era of the Brady and Belichick dynasty. The best players of the previous era are gone or aging. In these early days, the defining players look to include James White, Stephon Gilmore, Shaq Mason, Sony Michel, and Trey Flowers (though it's unclear if the latter will last). There's still time and a lot left to be written, but unfortunately the drafts of the last few years may catch up to them.
