The ancient Hellenes were very keen people, interested in all things nature, science and philosophy. They searched for answers to questions about their life, as well as the Theoi, and they theorized structurally about any discoveries they made, be it in health care, science or paleontology. Especially in the latter department, there are a few discoveries that might have shaped a large part of ancient Hellenic mythology and religion in general. Today, we'll be discussing some of those.

Giants:

Nichoria (Νιχώρια) is a site in Messenia, a regional unit in the southwestern part of the Peloponnese, Greece, on a ridgetop near modern Rizomylos, at the northwestern corner of the Messenian Gulf. It was the home of an Acropolis where many--what we now call--fossils were stored. The Nichoria bone was discovered by the ancient Hellenes roughly around 1000 BC. It is the blackened and petrified thigh bone of an extinct mega mammal--likely a woolly rhinoceros, or a mammoth--that roamed southern Hellas around one million years ago. The rusty-black color of the fossil bone indicates that it was most likely collected from the lignite deposits near the ancient town of Megalopolis, some 55 kilometers (35 miles) away from Nichoria. The Megalopolis basin was known in antiquity as the 'battleground of the Giants', where first the Titanomachy and then the Gigantomachy was believed to have taken place. The dense concentration of large fossil bones found at the basin inspired the belief that entire armies of giants were blasted by Zeus' thunderbolts, and the Nichoria bone--the distal end of a right femur, 15 cm (5-6 inches) wide, about twice the size of a regular human thigh bone--was most likely believed to have belonged to one of these giants. If the myth or the bone came first is unknown.

Cyclopses:
The one-eyed giants might have their origins in the recovered skulls of Deinotherium giganteum, which, loosely translated means 'really huge terrible beast'. Skulls and even tusks have been discovered in temples of the island of Krete, placed their by the ancient inhabitants. The Deinotherium is a distant relative to today's elephants. It stood about four and a half meters (15 feet) tall at the shoulder, and had tusks that extended over a meter (4.5 feet). It roamed Europe, Asia, and Africa during the Miocene (23 to 5 million years ago) and Pliocene (5 to 1.8 million years ago) eras before becoming extinct. As the image to the right shows, the large hole in the front of the skull was the anchor point for the trunk, not the eyes, but the skill of a young Deinotherium combined with the fearsome reputation of the cyclopses, makes it easy to see why the anciente Hellenes might have identified these skulls as belonging to Odysseus' captor.

Griffin's
The grýphōn (γρύφων) is a mythical creature with the body, tail, and back legs of a lion; the head and wings of an eagle; and an eagle's talons as its front feet. They feature in much Hellenic artwork, and Adrienne Mayor, a classical folklorist, proposes that the griffin was an ancient misconception derived from the fossilized remains of the Protoceratops found in gold mines in the Altai mountains of Scythia, in present day southeastern Kazakhstan, or in Mongolia. Looking at the skull of one of these dinosaurs, it really isn't a big leap; Protoceratops is about the size of a sheep or large dog, and they have a powerful jaw, and protruding bird-like beak. As a dinosaur, the rest of the skeleton would also have resembled a densely packed lion, one capable of carrying the weight of a man. The wings could simply have been assumed lost in time, or perhaps small bones found in the area would have indicated that the 'griffin' once took flight.

There are many more examples, and for anyone interested in this topic, Adrienne Mayor's book 'The First Fossil Hunters: Dinosaurs, Mammoths, and Myth in Greek and Roman Times' is an absolute must-read. From a review of the book:

"Above all, in The First Fossil Hunters Mayor proves two basic points: that many of the classic Greek and Roman myths did have a basis in fact, and that the basis for these facts were fossils. Using evidence collected from personal interviews, trips to Greek and Italian museums, and careful studies of classical myths and geology, Mayor continues to prove the two above points throughout her 360-page book. 

[...] Throughout her book Mayor continually proves the two basic points that she originally set out in the introduction: that many Greek and Roman myths had a basis in fact, and that these facts were often fossils. However, she goes beyond this basis thesis, and proves that Greeks and Romans frequently encountered the fossilized remains of mammals and dinosaurs, and that they developed very sophisticated concepts and myths to explain this bewildering and often confusing fossil evidence. Like their modern counterparts, Mayor writes, the ancient fossil hunters collected and measured impressive petrified remains and even displayed them in temples and museums. They attempted to reconstruct the appearance of these creatures through art and sculpture, and went even further in attempting to explain their creation and extinction."


Mammoth bone image source here; Cyclops image source here; Protoceratops skull image source here.