Taxonomy is the science of classifying species by assigning each species a degree of relatedness to other species. In general, the more alike one species to another, the closer together those two species will be classified. At its broadest, redwood sequoias and sunflowers and kelp are all considered to be plants, because they all share in at least one plant characteristic. At its most detailed, mastiffs and dachshunds and Shetland sheepdogs are all considered to be of the subspecies 'dog' (Canus lupus familiaris), because they all share in all 'dog' characteristics, and furthermore they can successfully breed with each other to produce fertile offspring which will also be 'dogs.'
These are examples of classifications which seem obvious. However, not all creatures fall so clearly into one set or another, even at the broadest level of classification. Taxonomy is an active and occasionally controversial science.
The taxonomic system still used today was originally developed by Carolus Linnaeus in the 18th century. He conceived of the living world as sets and subsets of organisms which could be classified in a seven-tier tree-style hierarchy according to their degree of physical similarity.
Today, the same seven tiers are still used, with two modern additions at the broadest levels: 'life,' and domain. Within those tiers, the degree and exact nature of similarity is constantly revised based on new field observation, palaeontological discoveries, DNA evidence, and even our understanding of exactly what constitutes a single species.
A multitude of subtiers are also used, such as subphylum. However, when giving the full taxonomic classification of an organism, usually only the basic tiers will be used: domain (if accepted), kingdom, class, order, family, genus, species. All the names are capitalized except the species name, and the genus and species are normally italicized. Most of the time it suffices to refer to a particular species by its genus and species names, e.g. Homo sapiens, sometimes with an added subspecies name, e.g Canus lupus familiaris for the common dog.
At the broadest level, modern scientific taxonomy begins with an unnamed, all-enveloping rank simply called Life'. All living things and debatably living things (such as viruses) fall within this rank. All non-living things fall outside it.
The next rank, and the newest, is domain. First proposed by Carl Woese, Otto Kandler, and Mark Wheelis in 1990, the modern three-domain system dividing between Archaea, Bacteria, and Eucaryota is now used by the majority of biological scientists. The intent of this structure is to distinguish between different types of single-celled organisms in a way that the old Linnaean plant/animal division never could. A fourth domain, Acytota, has been proposed for viruses, though it has not yet been widely adopted, and existing virus classification begins at the phylum stage. A large minority of scientists still holds to either a five-kingdom model or a two-domain (known as a two-empire) model dividing only between prokaryota and eukaryota.
The third rank, and the highest in the old Linnaean classification, is that of kingdom. Linnaeus divided simply between plants (Plantae) and animals (Animalae). Biologists who don't accept the domain structure commonly use a five-kingdom structure dating back to 1969, separating fungi (Fungi), non-nucleus single-celled organisms (Monera), and more highly structured single-celled organisms (Protista) from plants and animals.
Phylum is the highest generally accepted rank for viruses, and the fourth overall. For example, within the kingdom Animalae, animals are first divided into those which have spinal structures (Chordata) and those which do not (Mollusca, Nematoda, Echinodermata ...). The old Linnaean phylum of Vertebrata (animals with spinal columns) is now a subphylum of Chordata.
Next comes class. Within the old Vertebrata division, the class we share with dogs is Mammalia (mammals), which have hair, a four-chambered heart, and a neocortex in the brain. Other familiar Vertebrata classes are amphibians (Amphibia) and birds (Aves, sometimes combined with reptiles under Sauropsida).
Order is the tier where humans are separated from dogs. Dogs fall under Carnivora, whose digestive tracts can deal best with a primarily meat diet. Humans are classified as Primates, with five digits including an opposable thumb, a vision-dominated sensory system, and an enlarged cerebral cortex.
The family tier begins to define subtlies within the related species, such as the distinction between dogs (Canidae) and cats (Felidae). Humans, who have already been branched off in the tier above, belong to the order Hominidae, or great apes.
Genus may be the most controversial of all the taxonomic levels, especially since choices of classification at this level are linked most closely to the theory of evolution. One of the most recent attempts to cleanly define what should and should not fall within a single species suggested three major points of similarity, the primary one of which was monophyly, that all members within that genus should descend from a single ancestral taxon. There is also debate about the relevance of DNA sequences in classification.
Finally we arrive at the species tier of taxonomic classification. At its simplest, this level defines all organisms which are similar enough to be able to breed together to produce viable offspring within the same species. We may wish to add subspecies distinctions after this level, such as 'familiaris' for the familiar dog form of the wolf species. Especially among gardeners, the subspecies name can come to stand for the type of plant being sought.
While at the multicellular level these tiers remain relatively fixed, our understanding of individual categories within them does not. One familiar example of a reclassification based on new understanding is the 1993 reclassification of dogs from the Linnaean Canis familiaris domesticus, defining dogs as a unique species, to Canis lupus familiaris, shifting dogs to a subspecies of wolf. This shift does not indicate new knowledge so much as a willingness to objectively apply existing knowledge that dogs often successfully breed with wolves. Successful interbreeding is one of the markers of a single species. Ergo, dogs and wolves must actually belong to the same species.