Star jasmine (Trachelospermum jasminoides) is one of my favorite evergreen climbers. It looks beautiful all year thanks to its glossy green foliage, but by early summer it really comes into its own, producing masses of delicate, pinwheel-shaped white flowers with an unmistakably sweet fragrance. If you're looking to grow and care for star jasmine for year-round interest, June is when you'll really start to reap the rewards.
It's also one of the most important months for keeping the plant healthy. A few simple jobs now will encourage stronger growth, extend the flowering season, and help it cope if temperatures climb later in the summer. Whether you're training it over a pergola, up a sunny wall, or growing it in a large container to make your patio smell nice, these are the June tasks I'd never skip.