We show that Yangian x quantum group symmetries are realized in two-dimensional sigma models whose target spaces are three-dimensional squashed spheres, warped AdS spaces and Schrodinger spacetimes. These symmetries enable us to develop two descriptions to describe its classical dynamics, according to the left and right symmetries. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related one another through a non-local map.