I noticed this plant earlier this year, and as I usually do, let it grow until I could know what it was. Yesterday, when I was weeding in my garden, I started to pull out the vines which have beautiful, tiny purple and yellow flowers, and wide, heart-shaped leaves.
I stopped, thinking about how beautiful a vine it could be if I just let it grow on my fence. I decided to get an ID before ripping it all out. It turns out it is woody nightshade, a close relative of deadly nightshade or belladonna. While not as deadly as the more familiar belladonna, it is also toxic to humans and animals. When broken, it weeps a sticky, smelly sap. It has medicinal properties which have grown out of use.
As long as it is not eaten, it is safe. For a brief moment of insanity I considered leaving it, even knowing that it has the habit of overtaking gardens, simply because it is so pretty.