That's the theory. A practical difficulty, however, is that one can't test the theory from fossils. To really test the theory, one has to observe contemporary change in the wild, in the laboratory or at least reconstruct a detailed pathway that might have led to a certain adaptation. Darwinian theory successfully accounts for a variety of modern changes. Scientists have shown that the average beak size of Galapagos finches changed in response to altered weather patterns.
Mutant bacteria survive when they become resistant to antibiotics.
These are all clear examples of natural selection in action. But these examples involve only one or a few mutations, and the mutant organism is not much different from its ancestor. Yet to account for all of life, a series of mutations would have to produce very different types of creatures. That has not yet been demonstrated. Darwin's theory encounters its greatest difficulties when it comes to explaining the development of the cell.