I've decided to my review of the new Codex in a new way. I'll be going through the units much more briefly than normal, highlighting the changes to their rules and how I feel that will change how they're used on the battlefield. If you're looking for a more in-depth discussion of these units, check out my previous Space Marine Codex Review (which can be found here with a little searching).
The Warlord Traits have retained most of their old names, but the rules have for the most part been made much stronger.
Angel of Death: This still grants the Warlord (but not his unit) Fear, but it now forces tests on 3D6. This still doesn't get around the large number of armies that are immune to Fear but it does make it more useful against those enemies susceptible to Fear.
Imperium's Sword: This still grants the Warlord and his unit Furious Charge, but for it is no longer for just one turn. It's now for the whole game, and if any Space Marine unit is going to benefit from Furious Charge, it's the Warlord's.
Iron Resolve: This trait used to be one of the worst in the book, giving the Warlord's unit +1 to assault results. Now, the Warlord has Feel No Pain. Awesome upgrade!
Storm of Fire: This used to be a one use power, allowing a unit within 12" of the Warlord to re-roll failed to hit rolls when shooting. The new power grants a unit within 12" Rending shooting attacks, but can be used every turn. Even if the effect is a bit weaker, the ability to use it every turn is a big upgrades. Giving Rending to even a Tactical squad is great, but giving it to a unit of Sternguard firing Hellfire shells or a unit of Predators or Whirlwinds could win you the game.
Rites of War: This now allows all units in the detachment to use the Warlord's Leadership, rather than just those within 12". Another nice upgrade.
Champion of Humanity: This used to grant an extra D3 victory points if your Warlord killed the enemy Warlord in a challenge. This was absurdly difficult to pull off, and now it allows all friendly Armies of the Imperium units within 12" to re-roll failed Morale, Pinning, and Fear tests. Despite its short range, this makes units around the Warlord very reliable. A Warlord with Champion of Humanity makes an excellent anchor for your army.