Bring your container garden to new heights with flowering vines. Many vines, such as clematis, grow well in containers and provide color and vertical interest. They're also good for screening. Growing 6-8 ft. tall and very manageable, clematis vines are some of the most popular vines for sale for container gardening. They produce gorgeous, colorful flowers and have lush, healthy looking foliage. Other great vines for growing in containers are the Bleeding Heart Vine and the Climbing Shell Vine. When selecting flower vines to grow in pots, consider their light requirements, height, bloom time and hardiness zone. Like most other plants, vines require good drainage.