Martyrdom of the seven Maccabean brothers and their mother.
In a single move the Persians took over the Babylonian empire in 539 BC. That empire, of course, included Jerusalem, but their policies were such that exiles who wanted to return were allowed to do so. Some did. Work on rebuilding the temple began immediately, and after a hiccup or two was completed in 516. The city was also rebuilt, but the land remained part of the Persian empire until it fell to Alexander in 330. Soon after Palestine was under Greek rule, either from the Ptolemies in Egypt or the Seleucids in Persia. Cultural conflict, more than anything else, led to a local rebellion led by members of the Jewish Hashmon family, more popularly known as the Maccabees (‘hammers’). By luck or good strategy they were eventually successful, and so began the last independent Jewish state in Palestine until modern times.
In 66 BC the Romans under Pompey, responding to internal problems with the Maccabean state, stepped in and absorbed Palestine into their growing empire. Herod I was by far the most famous of the client kings in this period. Jesus was born, according to Luke, near the end of his reign (he died in 4 BC).
Of course, the Second Temple period lasts until the temple’s destruction by the Romans in the First Jewish War (70 AD), but is more convenient to break the timeline at the traditional division between BC and AD (CE).