The lecture hall partitions, $L_n$, are those integer partitions $(x_1, x_2, ..., x_n)$ satisfying (x_1)/n >= (x_2)/(n-1) >= (x_3)/(n-2) >= ... >= x_{n-1}/2 >= x_n >= 0. In 1997, Bousquet-Mellou and Eriksson showed that the number of partitions of $M$ in $L_n$ is the same as the number of partitions of $M$ into odd parts less than $2n$. This was viewed as a finitization of Euler's theorem that the number of partitions of $M$ into distinct parts is equal to the number of partitions of $M$ into odd parts. In this talk, we discuss joint work with Sylvie Corteel on variations and extensions of the lecture hall theorem.