Age of fossils in the past was generally determined by radio-carbon method and other methods involving radioactive elements found in the rocks. More precise methods, which were used recently and led to the revision of the evolutionary periods for different groups of organisms, includes

$A$ : Similarities in proteins and genes performing a given function among diverse organisms give clue to common ancestry.
$R$ : All the group of vertebrates arises from the common ancestor with great adaptation capability.

The scientist related with the over throw or the "Theory of spontaneous generation'' and experiments with swan-necked flasks is

The evolution of species is based upon sum total of the species adaptive changes preserved by