22nd of Tishrei in the Hebrew calendar and late September and October in the Gregorian calendar.
Shemini Atzeret and Simchat Torah are celebrated consecutively on the day following Sukkot.
Shemini Atzeret marks the start of the rainy season in Israel. On Shemini Atzeret Israelis pray for winter rains to begin.
On Simchat Torah the final chapter of Deuteronomy is read in Synagogue. It is followed immediately by the first chapter of Genesis, demonstrating that Torah study is an unending cycle. It is a day of immense joy in the synagogue. Traditionally the Jewish people dance and sing in the synagogue and in the streets.