For some people growing the common types of annuals and herbaceous plants is not enough to satisfy their interest and they need to specialize in a particular plant group. There are societies for every plant from roses to these fat plants. These plants are wonderful curiosities and are very popular among those plant collectors and growers that like odd or peculiar plants. I found an article by Geoff Stein over on Dave’s Garden website which gives you an insight into these unusual specimens.

The following is a brief introduction to these marvelous plants and a short list of the more common examples, including several of the easier ones to grow, in case one is interested in starting their own ‘Fat Plant’ collection.
What is a caudiciform?
This is any plant that forms a caudex, or a fat, succulent base/trunk/root. They are also referred to as ‘Fat Plants, or Fat-bottomed Plants’. Those with thick, fat stems/trunks with few branches are called ‘Pachycauls’. This swollen root or stem is used for water or food storage, allowing the plant long periods of survival without water or other forms of nutrition. Missing from the plant files is this description, which is too bad. Not all caudiciforms fit easily into the category of cactus and succulents, but most do. However, there are caudiciform trees (like Baobab trees), caudiciform vines (like morning glory relatives, members of the grape family, some passion vines) and members of the cucumber family, periwinkles, pelagoniums, milkweeds, yam family, and of course, cactus, Euphorbia, cycads and other succulents. There are over 100 genera of plants that have species that can at least loosely be described as caudiciforms.
Caudiciform plants can be divided up into 4 general forms: Phanerophytes are those plants that have an above-ground caudex and a growing center substantially (25cm or more) raised above the soil level, like this Dioon califanoi on the left (and most cycads), the Adenium swazicum (and all Adeniums, most Adenias, Beaucarneas, Cyphostemmas, and Pachypodiums etc.)
Chamaephytes are those plants with above-ground caudices but in which the growing centers are significantly closer to the ground (like this Euphorbia susannae on the left, and Dioscoreas)
Hemicryptophytes are caudiciform plants with a below-ground caudex, but the growing center is above ground (like this Ceratozamia zergozae on the left) The Boophane disticha on the right is actually a bulb, but is often grouped together with these other ‘fat plants’. These plants are cultivated to show off their caudex by raising it up- looks more interesting that way
Geophytes are plants that have both the caudex and the growing center underground, like this Ibervillea on the left and the Trochomeria on the right (as are most caudiciforms in the Cucumber family)

See more at Dave’s Garden