Yep, the shoot tips and young leaves. The older vines can be quite tough. I cook them like spinach. They are very common in West and Central African cuisine.

Do they taste like sweet potatoes? I have about a large pot full out there.

They don't seem to taste like much to me, just a 'green vegetable' taste with a slight bit of sliminess when cooked (nothing like okra though).

Maybe with a little salt and butter they would taste ok. Just curious. I never knew they were edible.

Sweet potato leaves are very popular in Asian & Pacific Island cultures. The shoots are sometimes sold in bundles in Asian markets. The good thing about that is, you can pinch off the tip & tender leaves, throw the stems into a glass half full of water, and cook the leaves. If you like the flavor, the stems will root quickly, and you can plant them.

Not all sweet potato leaves taste the same. I've tried some that were horrible, with almost a chemical aftertaste. The ornamental varieties with colored leaves fall in that category, among others.

Filipinos have an edible-leaf variety called 'kamote', which is the one I usually grow. In hot weather, the leaf production can be astounding.

But for a hot weather green, I much prefer the closely related water spinach. It too is often sold in bunches in Asian markets, and the shoots root even more readily than sweet potatoes. Water spinach can also be grown from seed, but unfortunately, it has been declared a noxious weed in the U.S., so seed is hard to find.

You can find a lot more info on both vegetables in the Asian Vegetable Forum.

oh...My parents survived from famine by eating them. That's what they told me. Food shortage is no long a problem when I was raised. But my mother occasionally prepare those food by steaming sweet potato leaves mixed with corn powder and seasoned with peanut oil. They are absolutely delicious. But my father don't like them possibly he just ate too much. LOL