Gradient flows have been extensively studied in the area of partial differential equations, with a wide range of applications. In this talk, we explore the relationship between gradient flows and De Giorgi's minimizing movements. We begin by examining the backward Euler method for minimizing movements in Euclidean space and then explore how minimizing movements converge to gradient flows in different spaces. Their implications for the well-posedness and long-time behavior of certain PDEs will also be discussed.