2-Piece

Diabolist

Hand of Gul'dan cast at full power summons a Demonic Oculus, up to 3. Consuming Demonic Art flings your Demonic Oculi at your current target, exploding for (457.103% of Spell power) Fire damage and (304.702% of Spell power) Fire damage to enemies within 10 yds.

Soul Harvester

Shadow of Death unleashes your  Demonic Soul to assault your current target for 12 sec, dealing (232.755% of Spell power) Shadow damage and (155.174% of Spell power) Shadow damage to enemies within 10 yds with each swipe.

4-Piece

Diabolist

Demonic Oculi analyze the battle while active and deliver information to you as they explode, increasing your Intellect by 2% for 10 sec.

Soul Harvester

Demonic Soul damage increased by 45% and  Wicked Reaping damage increased by 45%. Your  Demonic Soul generates 1 Soul Shard every 3 sec while assaulting enemies.

Diabolist Demonology Single Target

Diabolist Demonology Mythic + AOE

Soul Harvester Single Target Demonology

Soul Harvester Demonology Mythic + AOE

Intellect>Haste>Critical Strike=Versatility>Mastery

It is VERY important to note that this is a rough outline of desired secondary stats. Stat weights will vary from player to player due to varying gear sets and other external factors. The best way to tell what your own stat weights are is a raidbots.com Top Gear sim with Gems and Enchants taken into account. If you don't want to do that then you can just follow this.

Consumables

Enchants and Gems

The openers and rotations listed below are what you want to follow in a normal opener and setting. At times these may change due to fight mechanics or needing to hold CDs. 

Single Target Opener

1. Precast Power Siphon

2. Precast Shadowbolt

3. Grimoire: Felguard (if talented)

4. Shadow Bolt

5. Gloomhound/Charhound

6. Shadow bolt

7. Call Dreadstalkers

8. Demonbolt

9. Hand of Guldan

10. Demonbolt

11. Hand of Guldan

12. (Hand of Guldan)

13. Demonic Tyrant

14. Trinkets, Potions etc.

15. Demonic Strength 

Resume maintenance rotation 

AOE/Mythic +

1. Power Siphon if cores needed

2. Grimoire: Felguard (if talented)

3. Build to 5 shards

4. Charhound

5. Call Dreadstalkers

6. Demonbolt

7. Hand of Guldan

8. Demonbolt

9. Hand of Guldan

10. Demonic Tyrant

11. Trinkets, Potions Etc.

12. Demonic Strength

*Number of Imps will vary based off Demonic Core and Calling procs. For a more detailed breakdown, see below. A video guide is also provided.

 It is important to react to Demonic Calling or Demonic Core procs in your setup properly which change your shard consumption. It is worth practicing the opener to better learn how to approach them with Demonic Calling/Soul Conduit procs etc.

Maintenance Rotation and Implosion Rotation

Outside of your Tyrant setup, Demonology's rotation is very simple. You want to cast Call Dreadstalkers on cooldown while also casting 3 shard Hand of Gul'dans. You will never hard cast Demonbolt. All Demonbolt casts will be through Demonic Core procs.

1. You will want to cast your Charhound as close to on cooldown as possible in between Tyrant casts, as it is a very tight window with its CD being 25 seconds, and Tyrant being 1 minute.

2. Leave Soul Strike on auto-cast.

Implosion Rotation

When it comes to Implosion, it is a DPS gain in 3+ stacked targets. Your cue to implode is based on when your first set of imps are about to expire. A Weak Aura that tracks then is recommended for this purpose if you aren't familiar with the flow of Demonology. One can be found below in the Weak Auras section.

Doom Play/Maintenance

If you are playing the Doom talent, you will want to aim for as high of an uptime as possible in single target, which MAY mean holding a single Demonic Core stack for reapplication once the current Doom falls. You will also want to apply multiple Doom effects in Mythic + settings onto different enemies.