Phase five: post-emo hardcore? The "emo" style detailed above has been dead since around 1995, when new emo bands stopped forming and the old ones broke up. Most people in bands nowadays seem to regard pure emo to be overstated and quite cheezy (of course, this opinion has had its adherents all along...). The "emo scene" since has taken a few different directions. One is the ultra-heavy, ultra-fast wall-of-noise attack blending elements of grindcore and Neurosis-style apocalyptic chaos with bleeding-vocal-chords screaming: Jenny Piccolo, Union of Uranus, One Eyed God Prophecy, Makara, Living War Room, Orchid, Reversal of Man, Usurp Synapse, To Dream Of Autumn, etc.
Another trend has been to explore analog synthesizers and mod/goth/new wave sounds - post-emo style-rock? Das Audience / The Vue, VSS, Slaves, Crimson Curse, etc. Mostly a California thing originally, this has ballooned and is one of the vibrant growing scenes in indie music as I write this. The Faint, The Hives, The White Stripes, Milemarker, and even some mainstream music like The Strokes are reviving late 60s/early 70s rock and roll (Lou Reed and Velvets style, maybe a bit of Rolling Stones) with the emo fashion sense and a cynical underground sneer.
The vocal intensity of emo has been very influential on non-emo styles, as well. It has crept into new-school metallic hardcore quite a bit: Downcast, Struggle, Groundwork (AZ), Converge, Threadbare, Unbroken, Guilt, Botch, Fall Silent, Cable, Time in Malta. The chaos, power, and bleeding vocals of hardcore emo have similarly influenced non-emo ultra-hardcore bands: Jihad, Coalesce, Dillenger Escape Plan, etc.
Traditional East Coast hardcore and straight-edge has always been the most derisive critic of emo, befitting the male-oriented macho reputation of that scene. However, a few harcore/sXe bands have integrated emotional lyrics, octave chords, and a softer vocal delivery into their music. For example, listen to the later Turning Point, Endpoint, and early Lifetime records, as well as newer groups like Falling Forward, Split Lip, Shai Hulud. Many people with only a hardcore/sXe background consider these emo-inflected HC/sXe bands to be "emo" bands, but recognize the "emocore" category as detailed above as poppier and more rock versions of hardcore. They also tend to classify straight emo and hardcore emo as simply punk (based mostly on the low production values and the lack of heavy rhythms present in all HC/sXe). "Emo" is a catchall category for this scene - they classify almost all indie rock (Seam, June of '44, Codeine, etc.) and post-hardcore (Quicksand, Shift, Texas Is The Reason, Sensefield) as emo as well!
Screamo - I mentioned this under the "emo" section, however in recent years some bands have sort of re-integrated some diverse emo influences. With the band Saetia, for instance, you'll hear heavy fast screamed hardcore parts, with abrupt starts and stops and guitar focus more from the classic emo side, and quiet, twinkly melodic parts in between. "Screamo" has become sort of a catchall modern category for all of this for the few new bands playing this style, often used by younger fans who weren't around when the screaming vocal thing was new and unique.