We have never used it medicinally but its history includes to treat measles, tonsilitis, rheumatism, headaches, etc.
It is the state flower of North Carolina and is a popular garden plant even though it contains strychnine alkaloids and should not be consumed. Sensitive individuals can get a rash from the sap though I have not.
South Carolina says, "Here we refer to it as jessamine since that is how it is spelled in Joint Resolution No. 534, which established the flower as an emblem of South Carolina nearly a century ago.)"
The nectar is toxic to honey bees and can cause brood death.
Prune after bloom is the usual advice for keeping its size under control. You can see that it thrives in the half day shade provided by the carport. We rarely water or fertilize it and it keeps on going and growing.
If you have a vine and want to share it or want a vine and know someone who has one, layering is an easy way to make more plants.
Janet Carson at the University of Arkansas says to lay a lower branch on the ground and weigh it down with a rock. I usually remove the leaves from the stem portion that I want to root.
"Carolina jasmine roots fairly readily. An easy method is to layer one of the long runners while it is attached to the mother plant. You can actually almost weave it in and out of the soil, so that one long sprout could give you 3-5 new plants. Place a rock or brick over the part under the soil to keep it from bouncing up, and you should have rooted plants within a month or two. Once rooted, cut them apart and transplant. If you want to take cuttings, wait until mid to late summer to allow the cuttings to be semi-hardwood. "