Cactus Family. Everyone knows what a cactus is, yet they are so difficult to define. A cactus is a succulent plant that has a particular pattern: many combined and merged sepals and petals (tepals), often hundreds of stamen, and usually numerous stigma lobes. They are typically found in arid climates and most of them have sharp spines that are actually modified branches. While all cacti are succulents, not all succulents are cacti.