Suction (holdfast) discs
Scrambles; no means of attachment
If there's any kind of vine that gives the whole group a bad name, it's the clinging sort, which adhere tenaciously to almost any flat surface. Specialized structures let them grip their supports. Some, such as trumpet vine (Campsis) and ivy (Hedera), have stems equipped with aerial rootlets; others, like Boston ivy (Parthenocissus tricuspidata), have tendrils that terminate in suction (holdfast) discs.
Clinging vines are a good choice when you need to cover a wide wall. If you grow them on a fence or pergola, the stems will first attach to the surface; subsequent growth will pile up on itself, often resulting in the look of a twining vine.
Some vines have no means of attachment; they climb only in the sense that their stems will proceed on a vertical path if secured to a support as they grow. Left to themselves, they'll simply mound, sprawl, and scramble, though a few, such as climbing roses and most bougainvilleas, can hook themselves through adjacent shrubs or trees with their thorns. These vines will grow on almost any support as long as you provide appropriate attachment. Many gardeners cover flat surfaces with eyescrews and wire, then tie the plant in place at various points as it grows.