The new trailer which you can watch below, reveals part of the Siren's Mystical Assault skill tree:

• Phasecast - an Augment
  • Amara sends forward an Astral Projection of herself, dealing damage to everything in its path. THIS MUST BE EQUIPPED TO USE.
• Do Harm - a Passive Ability
  • Killing an enemy grants Amara a stack of Rush. Activating her action skill consumes all Rush stacks.
  • For every stack of Rush consumed, Amara’s Action Skill Damage is temporarily increased.
• Violent Tapestry - a Passive Ability
  • Applying an Elemental Effect grants Amara a stack of Rush. Activating her action skill consumes all Rush stacks.
  • For every stack of Rush consumed, Amara’s Elemental Effect Chance is temporarily increased.

Borderlands 3 - ECHOcast Twitch Extension

By linking their SHiFT account to Twitch, players will be able to participate in community events (like the rare Chest Event) and win in-game loot for BL3.

The next bit of new comes thanks to ResetEra. User vestan posted a link to a short BL3 gameplay clip. While the clip isn't particularly impressive there are quite a few nice details presented:

• Loot now has item scores (kinda like Destiny's light levels?)
• Guns have a handling stat now
• Amara's siren tattoos are orange in this clip, not blue (maybe they change depending on her action skill?)
• Grenades have symbols that reflect how they work
• New UI (looks slick IMO)
• New Claptrap voice (this isn't really a surprise - not a fan myself)
• Looks like they're going with the same scaling from The Pre-Sequel instead of Borderlands 2 (really nice change, imo)
• Weapon manufacturer chests across the board
• Handsome Jack is on a poster in the background
• Challenges are back
• Quest tracker