All organisms are classified by the science of alpha taxonomy into either taxa or clades.
To give an example, Homo sapiens is the Latin binomial equating to modern humans. All members of the species sapiens are, at least in theory, genetically able to interbreed. Several species may belong to a genus, but the members of different species within a genus are usually unable to interbreed to produce fertile offspring. (The red wolf Canis lupus rufus, however, may be a result of interbreeding between the grey wolf Canis lupus and the coyote Canis latrans.) Homo only has one surviving species (sapiens), Homo erectus, Homo neanderthalensis, etc. having become extinct thousands of years ago; some scientists argue for interbreeding between H. sapiens and H. neanderthalensis with fertile progeny. Several genera belong to the same family and so on up the hierarchy. Eventually, the relevant kingdom (Animalia, in the case of humans) is placed into one of the three domains depending upon certain genetic and structural characteristics.
All living organisms known to science are given classification by this system such that the species within a particular family are more closely related and genetically similar than the species within a particular phylum.
Since viruses are not living organisms, their classification is a challenging task. At first, viruses were classified according to their hosts: plant viruses, animal viruses, bacteriophages. Later, they were classified by the disease that they cause. For example, respiratory viruses, enterics. Now, viruses are classified based on the nucleic acid content, capsid symmetry and the presence or absence of the envelope.
Read more about this topic: Organism