Liandry's Torment is one of the most disgusting items in the game, but is often underrated. Its stats are nothing special (75 AP and 300 health LULW), but the two passives it has are immensely powerful when abused correctly. Let's have a quick look at some quotes from the wiki:

"Unique - Madness: Damaging an enemy Champion icon champion generates one stack every second for the next 4 seconds. Deal 2% increased damage for each stack, up to a maximum of 10%."
"Unique – Torment: Dealing ability damage applies a damage over time effect for 3 seconds that deals a total of 4.5% of target's maximum health bonus magic damage, with each tick of damage occurring every 0.5 seconds. This total damage is increased to 7.5% of target's maximum health against slowed or immobilized units, and capped at 100 damage per second against monsters."
Madness is a criminally underrated part of this item - a 10% damage amp after spending a bit of time in combat might not sound like that much, but it's crucial to remember that this applies to base damage as well as ratios for every source of non-true damage you have. Sunfire? Buffed by Madness. Autoattacks? Buffed by Madness. Base Damage on abilities? AP Ratios on abilities? Electrocute? Mana ratios on abilities? All buffed by Madness.

Madness is quietly giga busted because it stacks with pretty much everything multiplicatively. Hell, it even stacks with Torment, Liandry's other passive. It even stacks with other types of damage amplification. For example, Abyssal Mask + Liandry's in combination gives you a total of 26.5% increased damage when Madness is stacked.

Torment, on the other hand is much easier to understand and appreciate, with one exception - for some reason, cripples apply the empowered Liandries DoT. Depending on how well your champion innately empowers Liandries, it's very likely that you will need an item to help you apply the empowered burn. There are a few usual culprits which might come to mind here (Rylai's, Iceborn Gauntlet), but there's a third and particularly underrated option which occurs as a result of the cripple interaction: Frozen Heart. Notably, Iceborn Gauntlet and Frozen Heart are both "Tank" items, but as a result of Torment they become extremely valuable in an AP Bruiser's build. More on this in the "Iceborn Gauntlet or Frozen Heart?" section.

Some Grandmaster+ Ekko / Sylas jungle players (Arcsecond / King Nidhogg, respectively come to mind) pretty much follow the same build order every game:

Runic Echoes -> Iceborn Gauntlet -> Spirit Visage -> Liandry's Torment

Meanwhile, as of several buffs to the reworked Fiddlesticks he has emerged as a rare toplane pick with surprising effect, where he is frequently seen buying something to the effect of:

Frozen Heart -> Spirit Visage -> Liandry's + Hourglass (order up to personal preference)

In addition, I'm personally a big fan of the following Swain build:

Liandry's -> Frozen Heart -> Spirit Visage

Both cost 2700G and give 20% CDR
Iceborn Gauntlet gives 100 more mana than Frozen Heart - this works out to be something around 40% of a sapphire crystal, and is arguably pretty negligible.
Frozen Heart gives 110 Armor compared to Iceborn Gauntlet's 65- 45 more! this is the equivalent of a completed Zhonya's worth of armor.
Frozen Heart empowers Torment via a constant 15% slow field with similar range to level 1 Senna auto attacks, while Iceborn empowers Torment via a slow field applied by Spellblade, which also increases that autoattack's damage by 100% bAD.

If you assume that they have equal strength overall, it makes sense to buy Frozen Heart when you need lots of armor and when you don't intend on autoattacking much while Iceborn Gauntlet takes the lead when you can afford the armor loss and gain value from the stickiness/damage you gain from the Spellblade Procs.

= Both give 10% CDR and 55 magic resistance
- Spirit Visage costs 200 less gold than Abyssal Mask
- Spirit Visage gives 100 more HP than Abyssal Mask
- Spirit Visage gives 100% base HP regen, compared to Abyssal Mask's 0
- Spirit Visage increases all healing on the holder, including regen and vamp by 20%
- Abyssal Mask gives 300 mana
- Abyssal Mask gives the Eternity passive, which increases mana when damage is taken from champions and heals the caster up to 25 health per spellcast.
- Abyssal Mask applies an aura which increases the amount of magic damage nearby enemies (think Amumu E range) take by 15%.

As such, I personally believe Spirit Visage is better both for champions with any form of healing and those who do not like to "stand on top of" their opponents (battlemage bulids). Abyssal Mask is an item which should almost exclusively be used by champions who have very little long ranged damage and very little sustain - for example, champions like Amumu and Malphite come to mind while champions like Ekko, Sylas, Fiddlesticks and Swain would prefer Spirit Visage. In the case that you are playing a champion with no inbuilt healing and would prefer to stay at range, you're likely better off with either adaptive helm or (the admittedly boring) Banshee's Veil.

Builds like the above are strong on a wide variety of AP champions, but here are a few giveaways that your favourite champ might be able to abuse a build like the ones detailed above:
- They have high CC, but relatively low damage (Morgana, Neeko). This kind of champion can often benefit heavily from a Righteous Glory focused build, and is likely viable as a support.
- They're an enchanter who is on the cusp of being playable in another lane (Karma, Soraka). This kind of champion requires a bit more fiddling to find a usable build with - play around! ROA will help if you're struggling a lot in the early game, but remember that as an enchanter you gain more strength mid-lategame from healing/shielding power items than AP.
- They're an AP assassin who can thrive in fights if given a little bit more time to wreak havok (Ekko, Sylas, Fizz, Diana)
- They have lots of built in sustain (Swain, Fiddlesticks)