Integrable systems, both classical and quantum, kept reemerging in mathematics and theoretical physics during the past several decades. In this talk, after briefly reviewing classical and quantum integrable systems, I will focus on two recent geometric incarnations of integrable systems based on quantum groups, solved by the algebraic Bethe ansatz method. One is motivated by studying 2- and 3-dimensional supersymmetric gauge theories and mathematically explained through enumerative geometry of quiver varieties. Another comes from an instance of geometric Langlands correspondence. Finally, I will explain the relationship between these two geometrizations and discuss their applications.