We need to look at cacti generally.
Cacti originate from the Americas. Apparenty there is a Rhipsalis that is found in Africa. The only Cacti found outside America in a so called "natural" habitat.
Features:-
1) They have areoles - usually the small, often furry growth areas or points where new growth and or flowers emerge. note no spines on this second one, but minor indents make areoles. Also flowers emerging from areoles.(third picture) Many epiphytic cacti seem not to have major visual areoles.
2) They are perennial - That is they are persistant for more than two years. The Epicacti seedlings I grow, seem to take three or more years to flower for the first time.
3) The flower is a funnel shape (or wheel shaped) Petal number is usually many. The ovary forms below the flower.
4) The fruit is 'one celled' in the sense that seeds are scattered through out the mass.
5) When grown from seed, the seedings initial form is two cotyledons as do other dicotyledons.
So what makes these plants exciting to grow?
Well! some hybrids have huge flowers - can be over 10" in diameter.
The colour range is wide except for blues and generally they are easy to grow providing a few plant care techniques are applied.
They produce edible fruit and most do not have the spines or prickles that the standard cactus has, although they belong to the cactiaceae family.
The phenominial growth rates make them interesting. As they grow their appearance (in some plants) is 'sculpture-like' by the (again in some plants) wide flat branches. It has been suggested that the foliage looks like seaweed.