The belief in unknown and new animals has existed for a very long time, as evidenced by mankind's fascination with dragons, unicorns, and dinosaurs. The serious study of the fauna of earth, "Zoology" as it came to be known, was first established in the 1500's, and has since catalogued all familiar -- and quite a few unfamiliar -- animals on our planet.
For the most part, Zoology started off with the large creatures, and worked its way down: large obvious lifeforms like humans, lions, and whales were easiest to study and classify quickly. As the study continued, Zoology began to focus its hunt for new species more and more on smaller and smaller animals as it became popular belief that all large species had already been found and identified. At present, the majority of the Zoological efforts to locate and identify new species is concentrated in two ways: 1) the investigation of habitats not yet fully explored by man (rain forests, the oceans), and 2) study of tiny lifeforms that have a huge variety that has not yet been fully catalogued (insects and microscopic lifeforms).
Here enters Cryptozoology1, literally translated as "the study of hidden and unknown life." Cryptozoology is best seen as a sub-group of Zoology. While, like Zoology, it is interested in the study of biological lifeforms, Cryotozoology differs in that it is generally not interested in studying species that have already been identified, nor is it interested in small animal lifeforms; what Cryptozoologists study, research, and investigate is the evidence for a variety of large animals that are either presently scientifically unknown or presumed extinct.
Types of Cryptid
The animals that Cryptozoologists search for (referred to as "cryptids") fall into one of four large catagories that Chad Arment indentifies in his book The Search for Enigmatic Animals. The four catagories are:
1) Unknown animals that don't match the description of any known species, living or extinct.
2) Animals that are believed to be extinct.
3) Populations of animals of a known species, but possessing unexpected physical characteristics.
4) Unusual populations of animal found in unexpected locations.
Note that, for the most part, these catagories are concerned with populations of animals and not individuals. This is because an individual anomalous animal can be easy to explain -- a single kangaroo loose in the United States could be a recent escapee from a zoo; a population of kangaroos living wild in the United States would be far more difficult to explain.