The term ball cactus is usually applied to the species of: Parodia (syn. Notocactus), a South American cactus genus often kept as houseplants
It has also been applied to any ball-shaped cactus, notably plants from all of the following genera:
Coryphantha Echinocactus Echinomastus Escobaria Gymnocalycium Mammillaria Melocactus Pediocactus Turbinicarpus
And more specifically to:
Escobaria missouriensis, the Missouri foxtail cactus or common ball cactus Escobaria vivipara, the spinystar or purple ball cactus Gymnocalycium mihanovichii, the ruby ball or "moon" cactus Parodia leninghausii, the golden ball cactus or lemon ball cactus Parodia magnifica, the ball cactus or balloon cactus Parodia scopa, the silver ball cactus Pediocactus simpsonii, the mountain ball cactus