With the new Elemental Evil Player's Companion released awhile ago, Goliaths were added to 5e. I'm unfamiliar with 3.5 and previous editions, but I know that they were included and wielding large weapons was a thing you could potentially do.
Goliaths in 5e have the same trait as 3.5 it seems
Powerful Build. You count as one size larger when determining your carrying capacity and the weight you can push, drag, or lift.
So, does this mean a Goliath can wield large-sized weapons? The pushing/dragging/lifting capacity for a strong Goliath (say 16 str) would be nearly 1000 lbs (16 * 60) and the carrying capacity half of that. A heavy weapon weighs between 10-20 lbs, but this IS significant weight to be throwing around in battle, but I am unsure of the weight of a large weapon. My DM and I are unsure of the mechanics if a Goliath could. We talked about doing an extra die roll for damage, which is extremely strong, or treating the Goliath as if he were under the Enlarged Creature spell, which gives a +4 to damage, which seems more balanced in our opinions.
Are there rules for wielding large weapons in 5e? Can a Goliath wield large weapons out of the box with no feats?