The controversy between creation and evolution sets date before Darwin and Wallace’s theory of the origin of species by means of natural selection. Evolutionists argue that life forms of our planet possess a single origin and they have changed through a long geological period of time. On the other side, Young Earth Creationists are contrary to the idea of a planet having more than a few thousands of years and of the common ancestry of the living beings. The United States of America have a high percentage of creationists in its population and the main authors that write about this theme are from there. In the XX century, these two lines of thought disputed in the US courts for space in the education boards. The American Young Earth Creationism influenced many Brazilian authors and some of them deal with issues concerning geology and paleontology. To defend that the Earth has few thousands of years, these creationists need to deal with the current methods of dating. One way to get an approximate idea of ​​the age of a stratigraphic layer is using relative dating, which depends on three guiding principles of modern geology: the original horizontality, lateral continuity and superposition of layers. They argue that some phenomena as fossilized trees found vertically through several stratigraphic layers and thrust faults preclude relative dating. Another frequent argument states that in the fossil record, species appear with no trace of transitional stages between them, and this should be a problem for evolution. The existence of transitional fossils is also contested. Transitional fossils would be species well adapted to their environment without the "need" of modification. Living fossils are presented as species that have not evolved, therefore, implying that no other species have done so. This study aimed to clarify these misunderstandings about evolution, based on recent geological and paleontological findings. We explain how the principles of actualism are still up to date. How the sudden appearance of species on the fossil record is expected, given the geologic dynamics. There is a variety of organisms that are, indeed, transitional fossils, and we give the example of the early evolution of the tetrapods. They appear in the predicted geological time and right stratigraphic column, with the right morphologic characters, belong to the predicted phylogenetic group and are associated to a predicted fauna. We show how the so called “living fossils” belong to lineages that indeed changed through time.