Melodic metalcore or "Gothencore"
The music is a combination of melodic and heavy guitars, fast paces and the inclusion of some hardcore elements, such as mosh breakdowns and two-steps. Sometimes, other influences, such as Meshuggah-esque time signatures or softer (often considered "emo" influenced by some), melodically sung parts.
Although the melodic or "Gothenburg Death Metal" genre was pioneered by bands like At The Gates, Dark Tranquillity, In Flames, Edge of Sanity, and later Arch Enemy and The Haunted, it has spread beyond the Gothenburg, Sweden metal scene and has influenced such American bands like Lamb of God, Shadows Fall and Bleeding Through who also share stong roots in the early metalcore and hardcore scenes.
One of the most popular bands in the American category of this style would most likely be Killswitch Engage, who have been signed to Roadrunner Records, a relatively large metal label. Trivium is another band in the same style who have also recently been signed to Roadrunner.
Other notable bands in this style: Unearth,Atreyu,As I Lay Dying, Dead To Fall, The Agony Scene, It Dies Today, Darkest Hour and Undying. Poison the Well are often credited as one of the bands that made this style of metalcore popular with their full-length debut 'The Opposite of December... A Season of Separation', but some would say they also play almost too chaotically (see below) to be placed under this style, and others would say that they have over time progressed away from it, deciding to go in different musical directions with each album released.
Some gothencore bands include: Killswitch Engage, Still Remains, Trivium, Unearth, Atreyu, As I Lay Dying, Dead to Fall, The Agony Scene, It Dies Today, Darkest Hour, Undying, Poison the Well