Meristems are undifferentiated tissues that retain the ability to divide indefinitely and add new cells. There are three main types - apical meristems at tips that add new cells, intercalary meristems between tissues that allow elongation, and lateral meristems like vascular cambium that add girth. Apical meristems follow the tunica-corpus model with outer layers adding surface area and inner layers adding volume. Root apices have initial cells that form distinct tissue layers close to the tip or more open organization farther out.