Sparta and Athens were by far the two most powerful city-states in Ancient Greece (a.k.a Hellas). Both cities are understood to be democratic; however, Athens was definitely the more democratic of the two. Sparta was essentially state ruled.
Athens was located in the Attican region of Greece while Sparta was in the Laconian region. Athens was larger than Sparta with 140,000 residents in comparison to Sparta's 100,000; however, Sparta's army would have almost definitely been larger as military service was required of all men citizens.
In the first part of the 5th century, Sparta and Athens had been forced to cooperate with each other, albeit begrudgingly. During this time they worked as an effective team to repel a Persian invasion. Afterwards, however, relations between the two cities deteriorated quickly.
Because of their important political positions, both Sparta and Athens were looked up to by other Greek states. Athens headed up the Delian league numbering some 150 to 330 members. Sparta was joined mainly by states of similar Peloponnesian heritage, as well as those who were afraid of Athens' greatly growing power. Sparta's allies were primarily located in the south of Greece and were formed into the Peloponnesian League.
The tense relations between Sparta and Athens resulted in many battles being fought. The 1st and 2nd Peloponnesian wars included many of these. The 1st Peloponnesian War extended from 480 to 445 BC and resulted in a reasonably mutual arrangement being reached. The 2nd (or Great) Peloponnesian War was fought between 431 and 404 BC. After much fighting Athens was forced to surrender to Sparta.
As strained as their relationships may have been, Sparta and Athens were often compelled to work together for the common good of Greece.