Classical Greek philosophy is that portion of Ancient Western philosophy that begins with the end of the war against Persia in  479BC and ends with the deaths of Aristotle and Alexander the Great in 322BC. The previous period of philosophy is called Pre-Socratic, not because the philosophers all died before Socrates did philosophy, but because they were not influenced by Socrates and did not answer to his thought. The next period of philosophy is called Hellenistic, not because the Greeks previously did no philosophy, but because the efforts of Alexander the Great changed everything. Classical philosophy is focused on the philosophy of Socrates, those influenced by him and the philosophy produced by those people prior to Alexander the Great. There are a number of philosophical schools started in this time, as well as a number of famous philosophers.
In context, this was a history of relative freedom, especially in Athens, even while war happened on again and off again. During this period, the first historians appeared. Herodotus (484-425BC) was the first historian and the first to mention contact with India. Thucydides (460-395BC) was the first historian to promote something like the modern historical method. He wrote about the wars between Athens and Sparta. It was also during this period that a number of dramatists appeared, including Aristophanes who ridiculed Socrates in his play “Clouds”. Finally, this period was a period of scientific discovery. There was no distinction between philosophy and science, so these scientists are counted as philosophers during this time period. It was during this period that Hippocrates (460-370BC) established medicine as a discipline distinct from philosophy. Many discoveries were made in astronomy, mathematics, biology and geology.
Philosophically, the Classical period was one in which philosophy was establishing the very first schools of thought and learning to interact with previous philosophers. Most philosophers learned from a single teacher who would teach them everything they knew about philosophy. Like the previous period in philosophy, a lot of philosophers either did not write anything or their writings are now lost. Unlike that period, the writings of some philosophers are still around today. The range of opinions started at this time or continued from the previous period encompass almost every possible philosophical opinion imaginable. It was because of this that philosophers began to interact with previous philosophers.
Socrates, Plato and Aristotle are the most important philosophers of this time period. However, various other philosophers and philosophical schools are important. Antisthenes became the first Cynic. He believed in the pursuit of virtue against pleasure. Epicurus started the popular school of philosophy after his own name. He believed in the pursuit of pleasure. These philosophers and their schools either contributed to the development of later philosophy or were important in their own time.
This timeline indicates who was around at various times and which school of philosophy they belonged to.