Cactus require sand under them and light (Either Sunlight or Torches) to grow. They won't grow if there is no room above them. Cactuses can grow to 3 blocks high. Cactuses half a heart of damage the player on contact and destroys any item that touches them. When harvesting its advisable to destroy the bottom Cactus block so that the blocks above won't get destroyed when they touch the bottom block.