The compressionist does video encoding. They take the source files and compress them down to fit within the bandwidth of the Blu-ray disc. They're the encoders. I can't really say why they're great other than they do their job right. It's hard having to take a source file that can range from hundreds of gigabytes (TV episode) to multiple terabytes- going as far as 8 to 10 if it's a 4K or higher res source.
mp3dom works in Italy for the anime distributor Dynit, and has manually debanded source files frame by frame to make a better presentation (Madoka Magica, Fate/Stay Night UBW TV), as well as applying various filters to improve image quality, but uses the JP BD as a colour/brightness reference so he doesn't go too far from the intended look. He's produced several BDs that greatly trump their JP counterpart- A Silent Voice, Madoka, Fate/Stay Night, Kill la Kill, Your Name, Death Note, Yamato 2199, One Punch Man, Tokyo Ghoul, Gundam the Origin, Psycho Pass, Steins;Gate, Cowboy Bebop and many, many others. His new project- Akira, will be the definitive release. While it drops the "hypersonic mix", it allows for a bitrate increase to 35 mbps (compared to the 20 mbps of Bandai and FUNi), plus NO DNR this time.
Justin Sevakis owns Media OCD, and works with Discotek primarily, but has done discs for Anime Limited/@Anime, Sunrise, Bandai Namco, NIS America, Eleven Arts and Pied Piper. He's done every single Blu-ray for Discotek, so if you like what you see, he did it. Plus, he's the master of SUPER COMPRESSION. While mp3dom and David Mackenzie always aim for the highest bitrates, Justin is able to achieve similar results at bitrates often 1/2 or even 1/3 the size. His upcoming Lupin III Part 4 Japanese version BD has 13 episodes per disc, and he's guaranteed me it'll surpass the French encoded AL release on twice as many discs. His SD-BDs are just as great- being able to fit around 50 episodes at 480p with two language tracks on a single disc is quite a feat- however, his look better than their JP releases. Hitman Reborn has an upscaled BD in Japan by Pony Canyon across like 30 discs- Justin used 4 for SD quality, while retaining the correct frame rate, more detail, proper brightness levels,, and is English friendly at an actually affordable price.
David Mackenzie doesn't really do anime, well, he did do Metropolis (2001) for Eureka, but he's super f**king good. Like, DAMN. He's the god of Live Action compression. He primarily does work for Arrow and Eureka, but has done work for the BFI and some other Indie labels.
His BD of Carrie from Arrow has the whole film and extras on 1 disc. Why is that impressive? Shout Factory's US release was on 2, and David was able to nearly match it in average bitrate, while having higher spikes in bitrate, produce better video and audio quality, put all the same extras on the same disc, and add even more extras while loosing no quality, and in fact gaining quality due to better encoding! HOLY ****. He's currently working on all the Hong Kong releases by Eureka, which look unbelievable- for instance,
City Hunter (not the anime, the Jackie Chan film that's awesome) has 5 audio tracks: Cantonese Mono, 5.1 Mandarin Stereo, and English Mono and 5.1, yet he was able to add over 90 minutes of extras and still maintain an average bitrate of over 30 mbps.
If you're curious about how compression works, David did an excellent interview talking about the job- if you want to know a lot, it's a must watch.