We introduce the notion of quantum $N$-toroidal algebras uniformly as a natural generalization of the quantum toroidal algebras as well as extended quantized GIM algebras of $N$-fold affinization. We show that the quantum $N$-toroidal algebras are quotients of the extended quantized GIM algebras of $N$-fold affinization, which generalizes a well-known result of Berman and Moody for Lie algebras. Moreover, we construct vertex representations of the quantum $N$-toroidal algebras. This talk is based on the joint work with Professors Yun Gao, Naihuan Jing and Limeng Xia.