Generally speaking, when we discuss Ancient Greece, we're usually speaking about Classical Greece. If we're speaking about the Persian Wars, the Golden Age of Athens, or the Peloponnesian War between Athens and Sparta, for example, this is the time period we're speaking about. However, the larger scale of Ancient Greek history is far more widespread than that.
Personally, I would be inclined to divide Greek history into four general periods, with the first corresponding to the Bronze Age and Bronze Age civilizations such as the Myceneans. This would notably serve as a setting for so much of Ancient Greece's heroic literature.
The collapse of the Bronze Age (around 1200 BCE) threw Greek civilization and culture into crisis, resulting in the Doric Age (often referred to as a Dark Age). It was out of this context that the civilization of Classical Greece would gradually take shape and begin to emerge.
The third of these four general periods is Classical Greece. Finally, the last of them is the Hellenistic Age, which would emerge out of the rise of Macedonia under Philip II and the dramatic conquests of Alexander the Great (who died in 323 BCE). If you move further along this timeline, you'll observe the rise of Ancient Rome, which would come to dominate the entire Mediterranean and much of Western Europe with it.