The butterfly effect, as an icon for the chaotic dynamics, refers to the exponential sensitivity on the initial conditions. This phenomenon is common in daily life, e.g. it explains the difficulty of long time weather reports. For physicists, the idea of the chaotic dynamics helps to understand the ergodicity of a classical complex system and therefore is essential for the statistical mechanics and thermodynamics. In the microscopic many-body systems governed by quantum mechanics, the chaotic dynamics is also expected to be generic and ultimately helpful for the understanding of the quantum thermalization. What I will show in this dissertation is that the quantum butterfly effect could also provide precise information about the nontrivial properties of the many-body interacting systems, such as thermal transport and topological properties. I will employ two classes of solvable models: the Sachdev-Ye-Kitaev model in high dimensions and the rational conformal field theories in two dimensions to explicitly present the unexpected connection between the butterfly effect and other aspects of the model.