Immediately after the seven days of Sukkot, comes a very joyous two-day festival, Shemini Atzeret and Simchat Torah (in Israel they are compressed into a single day).
Our sages tell the analogy of a king who invited his children to a feast for a number of days. When the time came to leave, he said, "Please stay one more day; it is difficult for me when you are separated [from me].".
Candles are lit on both nights, Kiddush is recited, and festive meals are eaten. No work is allowed, nor is driving, writing, or turning electrical devices on or off. Cooking and carrying objects in public are permitted.
During Shemini Atzeret, one eats in the Sukkah, but the blessing for "sitting in the Sukkah" is not recited. The four species of Sukkot are not used. Yizkor is recited in the morning prayer.
On Simchat Torah, eating in the Sukkah is no longer done. On this day, the annual cycle of Torah reading ends and begins anew. The central moment of the holiday is on the night that begins Simchat Torah, when people joyfully dance in circles with the Torah scrolls.