There's a beautiful domed room just above that visitors see, but that's not where Tamerlane is actually buried. He's down here in the crypt, which is not normally open to tourists. However, a small bribe to one of the caretakers will get you in here to see the tomb of Tamerlane and several of his family members.
Tamerlane was exhumed by the Soviets just before World War II began, supposedly triggering a curse, but his body was eventually returned.