Based on cellular mechanisms, regeneration can be divided into two broad categories: 
1) morphallaxis and 2) epimorphosis.

Morphallaxis

Morphallaxis refers to the type of regeneration in which lost body parts are replaced by the remodeling of the remaining tissue.  In this type of regeneration, little or no cellular proliferation takes place during the regeneration process.  A classic example of an organism that regenerates using this mechanism is the hydra.  When a hydra is cut into two pieces, two hydra will be regenerated, both smaller than the parental hydra.  Once regeneration is completed, the two hydra can continue to grow and reach the size of their original parent.  Growth requires cellular proliferation but during the regenerative process very little cellular proliferation takes place.

Epimorphosis

In contrast to morphallaxis, epimorphosis requires active cellular proliferation prior to the replacement of the lost body part.  Epimorphosis can be further subdivided into dedifferentiation-dependent  and dedifferentiation-independent subclasses.  Planarian, which are flatworms, regenerate using a dedifferentiation-independent mechanism in which preexisting stem cells, known as neoblasts, begin to proliferate and migrate to the injured site in response to injury.  These cells then form a mass of proliferating cells, known as the regeneration blastema, that will later differentiate into the specialized cells that comprise the regenerated structure.  Most tissue regeneration in mammals also belongs to the dedifferentiation-independent subclass.  For example, mammals can regenerate their muscle, bone, epithelia of the skin and gut, blood, and some neurons by activating preexisting stem cells or progenitor cells.  Certain vertebrates, such as the salamanders (newts and axolotls), regenerate lost body parts through dedifferentiation-dependent epimorphosis.  In these cases, new stem cells or progenitor cells are created when differentiated cells reverse the normal developmental process and once again become precursor cells.  These dedifferentiated cells then proliferate and later redifferentiate to form the regenerated structure or organ.

Stem cells or progenitor cells are the common denominator for nearly all types of regeneration.  They either are already preexisting, as is the case for morphallaxis and dedifferentiation-independent epimorphosis or they are created by the process of dedifferentiation during dedifferentiation-dependent epimorphosis.

Note:  Although morphallaxis and epimorphosis are standard terms used by researchers who study regeneration, our use of the terms dedifferentiation-independent and dedifferentiation-dependent to subclassify epimorphosis is for descriptive purposes only and does not imply a general acceptance of these terms among the research community.  In fact, some researchers reserve the term epimorphosis to describe “dedifferentiation-dependent” regenerative events only and then add a third class known as tissue regeneration.  Other researchers, ourselves included, think that this practice is too restrictive, given T. H. Morgan’s original definition of the term epimorphosis.