Although we think of deserts when we think of cacti, there are a group found mainly in tropical America that colonised the trees. Epiphytic is the name given to plants that live on trees and we usually think about orchids living in trees but looking at the flowers, these are clearly cacti family. You can grow them in cactus soil but they are happiest if you grow them in bark chips in hanging baskets. I don't have enough trees to do that so mine live on a shady windowsill outside. All of these cacti would die in my greenhouse.
Epiphyllum, aka Orchid cactus have some of the showiest flowers in various colours and there are people who collect every colour. I think I only have two different kinds, the other doesn't feel like flowering so we wait... They only flower in spring
Talking about obsessive collecting of different coloured flowers, anther hoarder's favourite: Christmas, Thanksgiving and Easter cacti. They have those names in the USA or Northern hemisphere because they flower at those times. They are all also completely different species.
Hatiora gaertneri aka Easter cactus flowers in spring and has similar leaves but very different flowers to the Christmas and Thanksgiving cactus.
The Thanksgiving and Christmas cactus flower in late autumn and winter and are both Schlumbergeras but different species. Apart from the different flowering times, the Thanksgiving cactus has little points on its leaves and the Christmas cactus leaves have smooth edges. So now you finally can tell the difference!
Schlumbergera truncata aka Thanksgiving cactus is below
This one is Schlumbergera bridgesi aka Christmas cactus
The less common tree cacti are the Rhipsalis family
and they are unusual in that they are found in both Africa and the Americas. Rhipsalis is the only cactus species native to Africa. I'll only show the ones I have that flowered. They are all similar with slender stems with short hairs. This one is Rhipsalis pilocarpa
This last one is called Hatiora salicornioides aka Bones Cactus and it's in the same family as the Easter cactus
I hope some of the others I got flower soon, I'm curious what they look like. I've never seen these little cacti make seeds, perhaps they lack pollinators. They are extremely easy to propagate though although there's one type that I simply can't get to root, it always flowers and then dies on me without rooting. I can't figure out what I'm doing wrong with Rhipsalis ramulosa.