Oh god no, this one is difficult. Youtube, MP3 sharing sites, and many places really took off starting in the first decade of the year 2000. This means there are so many more amazing guitarists to sift through. They may not be famous or part of some hit band.

PLEASE NOTE: If you have a guitarists that began their activity during the decade in this post and you think they should be included, Please add a comment with their name and what you think is relevant about them and include a link to a video or some sort of media that you believe best expresses their virtuosity.

Virtuosity: When speaking of virtuosity we are speaking of technical skill. A musician may not be a virtuoso and master of the instrument and create a very influential body of music. That is not the scope of this particular series. It'd be infinite in size if it were. :)

Did you miss the previous decades?

If you missed the previous posts in this series here are links to them:
Part 1 - Pre-1980s
Part 2 - 1980s
Part 3 - 1990s

First decade of the 2000s

Gabriella Quintero

Gabriela Quintero -
Gabriela is one half of the band Rodrigo Y Gabriela and she may seem like an odd choice. It could seem that her particular role is not that technical, and that she is not virtuoso material. I could not do her parts if I tried to. It makes my wrist sore just watching her. I could do Rodrigo's parts. Gabriela is a master of particular style of rhythm and may be the best I've ever seen at it. She has given a short and sweet lesson on how to do her style, but that just makes me more impressed by it. So here you have a virtuoso of a specific rhythm style and one of the sole people to make my cut for something other than fast flying fret based fingers.
Tamacun

Guitar lesson - Right Hand Technique

Full Performance (2014) Live on KEXP

Marc Pattison

Marc Pattison -
I actually discovered Marc Pattison on a site back in the 2000s called mp3.com. He used to post these absolutely mind blowing guitar instrumental pieces. They were in the vein of Joe Satriani, but way more metal. I'd often have playlists of just his work playing in the background when I was coding and such. He does have a presence on youtube.com, but so many of his great pieces don't seem to have any representation there.
Chemical Burn - 3 Song Solo Playthroughs

Nucleus

Sentinel of the Matrix
https://soundcloud.com/marcpattison/sentinel-of-the-matrix

Christopher Amott

Christopher Amott - 1977-
Christopher is a Swedish guitarist and one of the founding members of Arch Enemy and Armageddon. He actually started in Arch Enemy in the 1990s, but his career seemed to explode in the early 2000s and is still going strong today.
A Solo

Armageddon - Equalizer - [Official Guitar Playthrough Video]

Jonathan Donais

Jonathan Donais- 1980-
Jonathan "Jon" started out in the band Shadows Fall and has been a guitarist in the band Anthrax since 2013.
Redemption Solo

Shadows Fall: Jonathan Donais (MMMW Guitarist Spotlight Webisode)
This is a video of him playing Ozzy Osbourne's Bark at The Moon which he is technically covering Jake E Lee's guitar part.

John Mayer

John Mayer - 1977-
There are people that believe John Mayer should be in this category. I am still trying to decide that myself, but I wanted to include him so that the post is not completely subjectively my taste alone. He does seem pretty skilled but I still have a lot of listening to do.
Slow Dancing in A Burning Room

Gravity

Omar Rodriguez-Lopez

Omar Rodriguez-Lopez - 1975-
Oh my god... I did not know this guys name, but I have laughed and enjoyed so many of the tunes from his band The Mars Volta. They are immensley enjoyable and so unique. Watching them perform a live show is a one of a kind experience. This guy is in the same category as Larry LaLonde from my 1990s part of this series. Both of them appear to be a chaotic mess when playing, but the fact they can precisely reproduce those sounds shows that what sounds like chaos is very deliberate. It takes a lot of talent to do that. It can be far more difficult than playing something that sounds normal.
Wax Simulacra

The Mars Volta - SWU 2010 Full Concert

John Frusciante

John Frusciante - 1970-
John is best known for being the guitar player for the Red Hot Chili Peppers from 1988 - 1992, and 1998 - 2009. It could be thus stated he has been around longer than the 2000s. In fact, the Chili Peppers have had different times in history where they are quire popular. He has produced and recorded with a lot of other artists.
John Frusciante - Top 10 solos

John Frusciante teaching different styles and soloing

Guthrie Govan

Guthrie Govan - 1971-
Guthrie has been in a number of bands and associations such as The Aristocrats, Asia, GPS, The Young Punx and he also won "Guitarist of the Year" competition from Guitarist in 1993. I didn't hear about him personally until he performed with Steven Wilson of Porcupine Tree fame. He is very cool IMO.
The Guitar Gods - Guthrie Govan: "Wonderful Slippery Thing"

Guthrie Govan - Fives at Jamtrackcentral.com

Michael Romeo

Michael Romeo - 1968-
He is the guitarist and founding member of one of my favorite progressive metal groups Symphony X.
Sea of Lies - 2006

Iconoclast Live in Los Angeles - 2015

There are quite a few covers of this song that I just showed you live on youtube. I want to feature a cover done by Luca Delle Fave who might show up in the 2010s if he is this good. He made this cover 2 days after the song was released. The only part he has wrong is that the initial part is a tapping part in the song. He does tackle the solo though which many people doing the cover ignore.
Iconoclast (Guitar Cover)

Steven Wilson

Steven Wilson- 1967-
Steven Wilson is a musical genius, producer, vocalists, plays many instruments. I do not typically think of him as a guitar virtuoso simply because his musical talents extend to so many places. He is the founder, lead guitarist, and songwriter of the band Porcupine Tree. I did find a video that is a collection of a lot of his solos. He perhaps does deserve to be here. If this was an amazing songwriter and composer blog he'd be close to the top. In later albums Guthrie Govan (above) picks up the soloing and he is more a virtuoso when it comes to a guitar than Steven Wilson.
Steven Wilson Guitar Solos: A Tribute

Steven Wilson How To Play The Blind House

Conclusion

It is very difficult to find specific guitarists on youtube. I know there are some great guitarists from the 2000s that did not make my list. I hope you all will post some names and examples of work to flesh this out.

I am going to stop here for this blog post. It is quite long already. If there are votes and interest I will continue where I left off and do another post starting with the 2010s.