Striking features of the structure of the plants, such as the presence of stems.
Whether or not the individual carpels are joined to each other at the base.
The shape and surface appearance of the pollen grains.
The shape and size of the seeds.
The ability of the plants to hybridise.
Distinctive features of the leaves, such as the degree of dissection and their hairiness.
Flower colour

Brian Mathew, in his invaluable monograph, has divided the genus into six sections:

Syncarpus The name refers to the fact that, uniquely among hellebores, the three carpels are joined together for half their length. This section contains just one species, H. vesicarius, which is quite different from all other species. No hybrids involving this species are known.
Griphopus The name is derived from gryphos (a gryphon) and pous (a foot) and relates to the resemblance between the narrow leaflets and the feet of a gryphon. This section also includes just one species, H. foetidus. Occasional hybrids with the species in the following section have been re-corded but are not fertile.
Chenopus The name derives from the Greek chen (a goose) and pous (a foot) and describes the leaves, which are divided into three broad leaflets. The two other stemmed species, H. argutifolius and H. lividus, belong here. When crossed, the two species in this section produce fertile offspring. They have sometimes been treated as one species.
Helleborus The ancient Greek name for the plant, and probably originally applied by them to H. cyclophyllus. Much later, botanists made the very distinct H. niger the type species of the genus, and so the section containing it must carry the genus name. H. niger produces infertile offspring when crossed with the two species in the previous section.
Helleborastrum The name indicates a similarity to, but not an exact likeness with, plants in the section Helleborus. This is by far the largest section and contains the following nine species, all of which cross with each other to give fertile offspring: H. atrorubens, H. croaticus, H. cyclophyllus, H. dumetorum, H. multifidus, H. odorus, H. orientalis, H. purpurascens, H. torquatus and H. viridis.
Dicarpon The name of this section was derived from the fact that its only species was thought to be consistent in having just two maturing carpels. There is just one species in this section, H. thibetanus. Its ability to hybridise with other species is, as yet., uncertain.