On November 21 2004 Nintendo released the Nintendo DS for $150. It was technically their second handheld with multiple screens. The first being the Game & Watch (covered in pt 1: https://imgur.com/gallery/Sx6yidb). As well as being a full 3D capable handheld, it maintained backwards compatibility with all GBA titles.
Nintendo incorporated many of the features that Tiger's Game.com (covered in pt 2: https://imgur.com/gallery/Wmkv6Uj) had in 1997, including the touch screen, stylus, and internet connectivity. Though these features were much better executed due to the advancement of technology.
Unlike the GBA, the DS featured a built in operating system that managed the time, launching games, internet connectivity settings, and had a built in application: Picto-Chat, an IM client that allowed you to also send drawings/hand written messages to friends.
Over 3400 games were made for the DS with notable titles including: New Super Mario Bros., Tetris DS, Ninja Gaiden DS, Guitar Hero, Animal Crossing: Wild World, Nintendogs, multiple Castlevania games, Megaman ZX, Okamiden, Pokemon Diamond/Pearl/Platinum, Pokemon HeartGold/SoulSilver, Mario Kart DS, and many, many more...
Current Nintendo president at the time: the late, great, Satoru Iwata said, "We have developed Nintendo DS based upon a completely different concept from existing game devices in order to provide players with a unique entertainment experience for the 21st century."
This first iteration of the system was later affectionately dubbed the "DS Phat" after the DS Lite redesign released 2 years later.
It would go on to sell over 154 Million units.

Released in late 2004 the Game King was a GBA knockoff made by Chinese company Guangzhou Panyu Gaoming Electronics Co
About 20 games were created, mostly clones of existing titles and were sold on 4-in-1 cartridges.

In 2005 Nintendo released the final Game Boy system. The Game Boy Micro is the 2nd smallest cartridge based handheld they ever produced. Barely larger than the GBA carts you plugged into it, it was promoted as a budget alternative to the DS priced at $100.
It had swappable faceplates you could purchase to personalize your Micro. Another downside was the removal of backwards compatibility for OG Game Boy and Game Boy Color games.
It sold over 2.4 million units, well under Nintendo's projections. Iwata later admitted the DS hurt the sales of the Micro.

Sony, no longer content with only dominating the home console market for two generations in a row, finally decided to enter the handheld market in 2005 with the launch of the PlayStation Portable. Costing $100 more than the DS at $250, it boasted much more powerful hardware, a massive 4.3in screen, and many multimedia features the DS was lacking such as: music and movie playback, built in web browser, and a USB port for PC connectivity.
Games came on Sony's UMD (Universal Media Disk) which was a sort of CD/cartridge hybrid. Despite its name it was only ever used on the PSP. Over 1700 games were made for the PSP with notable titles including: Crisis Core: Final Fantasy VII, Megaman Maverick Hunter X, Metal Gear Acid, God of War: Chains of Olympus, Daxter, Monster Hunter Freedom, Phantasy Star Portable, and many more.
The PSP could also connect to the PS3 via wi-fi to use the PSP screen to play games on your PS3. It also had component and composite adapter cables to connect to a TV.
Eventually a large homebrew scene developed for the PSP despite many efforts from Sony to break users of the habit.
It would go on to sell over 76 million units.

Released in early 2005 in the EU and then later on in the year in the US, the Gizmondo was an ambitious handheld created in response to Nokia's N-Gage (covered in pt 3: https://imgur.com/gallery/jaKhYbi).
Priced at £229, the Gizmondo featured full 3D graphics, movie and music playback, web browser, camera, and SMS messaging. The world's first ad supported system, the Smart-Adds enabled device allowed devs to show users ads in order to keep the hardware costs lower. A non Smart-Adds version was available for $400. There was also a GPS add-on.
Only 8 of the 14 planned games released for the system.
The company announced a wide screen version shortly before launch, resulting in low sales.
Leading up to the launch of the system, Gizmondo would host an infamous celebrity party in an expensive London hotel trying to promote the device, as well as sponsored a race car in a 24 hour race.
The Gizmondo's problems were compounded by the reveal of involvement of several of their executives in Swedish organized crime...
In 2007, GameTrailers named it "the worst console of all time." and worst selling handheld in history by GamePro.
It sold less than 25,000 units after being discontinued less than a year later.

GamePark would release the GP2X, a Linux based followup to the GamePark 32 in September 2005. The GP2X is designed for homebrew developers as well as commercial developers.
It is commonly used to run emulators for game consoles such as Neo Geo, Mega Drive/Genesis, Master System, Game Gear, Amstrad CPC, Commodore 64, NES, TurboGrafx-16, and MAME.
An updated version of the system was released in 2007 that featured a touch screen.

Nintendo released a sleeker version of the DS in 2006 for $130. The DS Lite was about 2/3 the size of a DS Phat and boasted a brighter screen. Despite being a smaller unit overall, the DS Lite's stylus was slightly larger than the orginal's.
The launch of the DS Lite mirrored that of the SNES in Japan, with stores selling out of the initial print run of 550,000 units in a matter of days. The shortage was supposed to be eased after Nintendo released an additional 700,000 units during April 2006, however, retailers in Tokyo sold out yet again by late May 2006.
This shortage would last for most of 2006 and 2007 with retailers all around the country having permanent signage apologizing for the shortage and stating that the arrival time of new stock was unknown. Since restocking was erratic, looking for the product often involved several visits to multiple different stores, usually unsuccessfully. This was still the case in Japan as of April 25, 2007, with stores turning away potential customers every day and selling out quickly.
It was much easier to find in the US for some reason.
Nintendo opened a new branch, Nintendo of Korea, on July 20, 2006. The DS Lite was the first system to be released in South Korea by the subsidiary,] being released on January 18, 2007. Popular Korean actors were enlisted to help promote the it. NoK stated they had sold more than one million units in the first year of sale with around 1.4 million sold as of April 2008.
Part 1: https://cohost.org/AgentOtter/post/5565885-a-brief-history-of-v
Part 2: https://cohost.org/AgentOtter/post/5584876-a-brief-history-of-h
Part 3: https://cohost.org/AgentOtter/post/5599570-a-brief-history-of-v
