Cacti can only grow on sand, up to a maximum of 3 blocks. Cacti cannot be placed next to another block. When harvesting the bottom, the whole cactus breaks, since it is an entity. Cacti doesn't need light to grow.
As a crafting ingredientEdit
Cacti needs to be placed on sand, but cannot be placed next to another block. When mining, destroy the bottom cactus block so all the cacti falls and doesn't get destroyed.