The build I used to get the world first solo monk GR59 clear. There's a link to Natsuma's video guide on the build at the bottom.
The build relies on heavy Resource Cost Reduction to get as many dashing strikes as possible. It relies heavily on two not-so-well known things. First that I'm fairly sure Dashing Strike has a much higher chance to proc Flying Dragon compared to generators, and second that Obsidian Ring of the Zodiac is awesome and with enough IAS, CDR and RCR gives you a 100% uptime on Epiphany, Inner Sanctuary and the Breath of Heaven spirit generation buff. It is very strong for T6 farming, medium greater rifts and for pushing high greater rifts, so basically everything.
The build's defenses come from Spirit Guards, almost 100% uptime of the Flying Dragon proc combined with the really fast speed of Dashing Strike for insane Life on Hit and a 100% uptime on both Epiphany: Desert Shroud and Inner Sanctuary.
There are three variations of the build I use depending on what I'm doing. One for T6, one I change items around for medium GR farming and one for pushing.
For items I swap out Spirit Guards for Nemesis Bracers, gloves for a pair of Fists of Thunder with attack speed and possibly Hellfire Neck depending on the passive and stats (RCR on neck is very viable for T6 as well).
For skills I swap the rune on Epiphany to Insight, Inner Sanctuary you can swap out for a skill of choice, I usually take Mantra of Healing: Circular Breathing (for lazyness) or Sweeping Winds: Inner Storm for some passive spirit regen for when Epiphany drops, and Mantra of Salvation to Cyclone Strike: Implosion.
For passives I use Exalted Soul, Seize the Initiative, Beacon of Ytar, Guardian's Path and either Alacrity or Chant of Resonance if using Mantra of Healing. You could change some paragon points from Dexterity to Movement Speed too if you prefer.
The basic idea for T6 is to spam Epiphany and Breath of Heaven on cooldown, dash like a crazy person and kill everything in sight. When something (usually elites or RG) doesn't die instantly, alternate your generator while dashing in place. Depending on mob density you either alternate walking with quick dashes with low density or spam your generator with shift pressed while dashing constantly when there's enough density to keep spirit up. Because of the low resource costs and almost constant uptime on the Flying Dragon proc, this build when played properly can make the godbuild look like a snailbuild
- Mid GR farming
I usually swap out defensive passives and skills out of the T6 build depending on the rift level. With my gear I usually swap back to Spirit Guards and Vitality first, next Inner Sanctuary instead of Mantra of Healing or Sweeping Winds, then Harmony passive, and I try to keep the Insight rune on Epiphany up to GR47-48. Insight is not required at all, but it makes the build play a lot smoother between packs mostly.
The idea is similar to T6, you dash around like a madman, look for good density, cyclone strike mobs together, pop down an inner sanctuary and dash in place until mobs are dead, while just spamming Epiphany and Breath of Heaven mindlessly (assuming you have enough CDR/IAS/RCR).
To give you an idea of the clearspeed, with my gear I usually clear GR45-48 in 3-5 minutes or so. Even managed a GR42 clear in 1:15 when I was around paragon level 600, which was fun, most 42's were around 1:30-3:00 at that point.
- High GR pushing
There are a few variations I tried, the one linked is what I used to beat GR59. It has good survivability, but if your Epiphany or Inner Sanctuary drop for more than a few seconds you will die horribly. A few possible variations are using Cyclone Strike instead of Mantra together with String of Ears, but the damage and survivability loss are probably not worth it. The 5th passive I used was Guardian's Path for the extra spirit generation, so any of these 5 passives on your Hellfire Amulet is good.
The build relies on fast movement to skip mobs, high survivability to facetank most of it, and high damage from the high spirit generation and cost reduction together with an almost 100% uptime on the Flying Dragon proc.
As with most GR pushing builds, it's fairly reliant on good RNG for mobtype and density. It doesn't rely on Pylons much though. Because of the high RCR, high survivability, high movement speed and low base damage, Conduit doesn't even tickle mobs, Speed pylon is pointless, Shield pylon is situational at best, Channeling pylon isn't as good because of all the RCR and lower DS damage and Power Pylon is around 200% damage only because of permanent Taeguk, Forbidden Palace and DS damage on gear, so it will save you just over a minute tops.
It's absolutely essential to keep Epiphany up at all times, if it drops for more than a few seconds you will likely die horribly. Same for the Spirit Guards buff which is easier to keep up. Dash around, skip bad density, completely skip the worst density/mobtype levels, that should take less than a minute even for the medium-sized levels because of the low DS cost. Once you find a decent density group, charge in, drop a sanctuary and alternate your generator with dashing in place. Be careful with dangerous packs, get out when you're in too much danger especially if like me you didn't take Near Death Experience. For the boss just keep sanctuary, epiphany and breath of heaven up and just go ham dashing in place on him. Just as important for this spec, maybe even more so, is making sure you never let your Dashing Strike charges run out. If you do, you're useless for up to 4-5 seconds, which means a lot of wasted time, but more importantly a lot less LoH and no dashing away during that time, very often leading to death. You will also want to try and manage your FD procs some, by trying to stay medium-high spirit when the proc is up and spamming DS until low spirit when it goes down to get the proc back up as soon as possible. A dropped Flying Dragon proc at the wrong time can and will kill you from lack of Life on Hit.
Another thing to keep in mind for pushing: deaths are bad. When you die you lose your Taeguk Stacks, losing you precious damage until they're back up, but more importantly you will need to use Epiphany and Inner Sanctuary right away to keep from dying before any Gogok stacks, which if things go bad means downtime on Epiphany and/or Sanctuary before the first reapplication, possibly leading to a chain of deaths, that and you start on low spirit with no Flying Dragon proc up, leaving you even more vulnerable.
A few other notes for the build. As with any other builds when pushing GRs it's very important to get to know your mobs and the progress they give. There don't seem to be a lot of guides or lists for progress, but I found http://us.battle.net/d3/en/forum/topic/15269358546 to be somewhat helpful, no idea how up to date or correct it is, but it seems to give a general idea of what mobs are terrible and which are good. In general, zombies, moonclans, act 5 reventants (skeletons), unburieds (the spiky big A1 mobs) and to a lesser extent large skeleton packs seem to be the best by far. Mobs like fallen minions, scorpions, mallet lords and many others are pretty much always skip.
For fists of thunder it looks like the third hit is slower than the first two. Considering the negligible damage the generators do in this build, I did some testing. I'm not completely positive, but it looks like skipping the third hit when possible seems to increase overall damage by 10-20% or so. It's not a major deal in most cases, but when possible I try to dash often enough that it interrupts the generator sequence before it gets to the third hit, so FoT, FoT, DS, FoT, FoT, DS or FoT, DS, FoT, DS.
Last a note about Resource Cost Reduction. To many it will probably be tempting to replace some or all of the RCR with damage stats like crit chance. You might be able to get away with 1-2 slots, but any more and you will lose too much uptime on your Flying Dragon proc and might get you downtime on your defensive cooldowns, which leads to deaths, which in turn lead to more deaths.
I hope you all enjoy the build as much as I do, I certainly enjoy playing it a lot, both for farming and pushing high greater rifts, and good luck to everyone aiming for high ranks!
Natsuma's video guide on the build: Link