@Blowfeld
Thanks for the +1 and thanks for finding that for me :D
just quickly glanced at your guide and I liked it so I gave you a +1 also.

I totally love the layout of your guide which is definitely better then mine...

This makes me give you +1 for the better arts approach.

PS: It is "runes" not "ruins" in that first paragraph of RUNES ;)

Banshee's is usually a must regardless of team composition. It's bonuses are just too nice to shut out just because it has magic resist too. Also, if you were to get mallet and banshee's, it would bring up the damage output of atma's, making it viable yet again. I must press the issue. IE is nice, but way too expensive compared to the minor lack of bonuses from atma's for a much better price.

@blaisem
There are 2 reasons i buy youmuu's and I will be adding these into the guide shortly. The first being that its movespeed bonus can be a lifesaver sometimes and the second being that it will help you take down towers. Press R, activate yomuu's and watch the tower drop.
The reason why I said to grab an IE was just for the extra attack damage. Of course you could buy any other item instead if needed but if you're looking for more damage since you already have a bloodthirster I choose IE. I used to have atma's impaler in the guide but then I realized that you don't get you're money's worth of damage form it by just having a Frozen Mallet. And for the guardian angel I sort of let that fill the place of the defensive item and i put it in the build because that's what I would get versus a balanced team however, if I was facing a heavy Magic or Physical team i would pick up a Banshee's or Thornmail instead of the Guardian Angel.

Interesting guide. I liked your reasoning behind not using a trinity force. Riven does a lot of burst damage with her abilities. Since most of her damage comes from them, they scale with bonus AD, and they don't seem to proc on hit effects(true?), then crit and attack speed aren't necessary, just bonus damage to synergize with her abilities for maximum damage output.

My question is: Why Youmuus? It adds crit, it's active adds attack speed and movement speed. Riven is already has decent escape with 2 abilities giving a dash. Youmuu's relevance to Riven is essentially in +30 damage, 15% CDR and +20 armor pen. Nice for early game, aka brutalizer, but why upgrade?

I was thinking, what do you think of trading the ghostblade for a last whisperer? If the opponent buys one thormail, even without armor seals, they can easily reach 170 armor. Even with easily reached lesser armor like a chain vest, with runes they still have hefty armor (120-130). 20 armor pen isn't what you would want. You would want 40% armor pen. You can take ionian boots to make up for CDR. Flat pen doesn't scale well with % armor pen. Since you won't be relying on flat pen, you might as well change runes to AD marks/quints.

Finally, you recommend replacing the lantern with an IE. IE adds 80 damage and gives awesome crit. If Riven is going to rely mainly on abilities, crit isn't essential, so why not get an atma's impaler instead? You do keep some of the crit, and you get +60 damage instead of +80, but you gain +45 armor. Now you can sub your Guardian Angel for a Banshee's Veil. In total, you end up with 23 less armor, but 12 more MR and 375 HP. With mallet you reach 3k life and with, say, flat armor seals and MR/level glyphs you get around 130 armor and 115 MR, keeping you at 50% or above damage reduction against armor/magic pen runes. Coupled with your E you have strong survivability.

The biggest advantage with veil is you protect your Q combo from stun interrupts. If you hit all 3 of your Q combo, you more than make up for keeping IE for +20 damage, 7% CrC, 50% CrD and risking only landing 2 hits on combo - or getting stunned on approach! So buying veil protects your Q and can block a few hundred points of damage in a spell, resulting in ultimately a significant increase in your damage output and stronger survivability. I think this may outweigh the armor loss, to be honest.

You still end up with 350 AD with AD marks/quints and full BT (250 bonus AD, which is monster and will make your E and other abilities really strong) and 3000 life with decent armor/MR. Plus these suggestions are cheap to build, total build costs would be at like 14.5k or something if I did my math right, which means you will often complete it. Seems almost OP :/ Anyways, those are my thoughts on Youmuu's, IE, and Guardian Angel for Riven.

@ice101v
The reason I pick up a wriggle's is for it's early/mid game benefits.
During early game the extra damage helps all your spells and the armor and life steal give you some nice durability and sustain. The free ward can also help you from being ganked.
During mid game the passive on wriggle's lets you kill creeps faster making it easier for you to push lanes and farm up cs.

I don't see the appeal of wriggles. I would rather save the money for BT. I usually get brut > phage > BT then frozen mallet/qss. Depending if its a balanced team or heavy AP.

Thanks for the comments guys. Just to remind everyone that the item build is to be used as an outline. One of the best things you can do as a league of legends player is to learn to adapt to different situations, that is to say if you find yourself dying often before you get to the bloodthirster it might be a good choice to switch it for a different item. I'm working on the 3.0 changes currently and I'll post them up as soon as they are done :D

good guide (Y)

It looks nice. I can't wait to try it. :]

I upvoted this guide just because there is no trinity force in your build!

Looks pretty good. Straight and to the point. Best riven guide I've seen so far. +1