Bittersweet is a vine from Asia (there's a type native to here but I've never seen it) that grows in sunny conditions. It loves forest edges where it can scramble up trees. If you've looked at the sides of highways late summer and seen masses of vines smothering the trees, that's bittersweet.
It's important to get it out of your yard because it will truly take over, killing your trees and smothering your other plants.
The easiest way to remove it from your yard is to spot the seedlings. They are upright little plants with light green leaves and a yellow root when very young, orange at maturity. The root is the easiest way to identify the plant. If you've ever pulled a mature vine, you know that its bright orange root goes underground forever.
If you see something that might be bittersweet but aren't sure, pull one up and check the root. Better to pull one wrong plant than let your yard be overtaken. Plus, I learned to identify bittersweet by pulling large vines and associating the leaf forms with that root, so it helps you learn the plant.
If you've got larger vines, you'll have to decide whether to dig them out or clip them at the ground. Digging is more thorough, but it disturbs the soil, and if you've got other undesirable plants around, they could colonize that space. Clipping growth at ground level 6 times a year will eventually exhaust the root without disturbing the soil.
And these vines spread through birds eating the berries and dropping them around. This winter I saw red/orange berry husks in the snow and knew they were bittersweet seeds. I got a plastic spoon and scooped them into the garbage, which is totally not weird.
So, do your best in the fight against bittersweet. If we all monitor our own yards, it prevents further spread of the vine.