Two-weapon fighting is now an option for all classes. although fighters have the ability to utilise the two-weapon fighting style.
Without that fighting style, the player can wield a light weapon in both hands. Light weapons include: daggers, clubs, handaxes, light hammers, short swords, scimitars, and sickles. The weapon in the player's main hand works as normal but the weapon in the off hand can make a single attack per round as a bonus action only without any bonus damage from stats and the like.
If a fighter takes up that fighting style, then both attacks are made with normal bonuses to damage.
It hopefully adds a bit of flexibility to builds and weapon choice in the early game and it seems like it could really come into its own if you manage to track down two powerful light weapons to use together.