Abstract: In this talk we are going to speak about random product of isometries chosen by a sensible rule. One of the dynamical characteristics of this product is its drift, which describes the average displacement rate of the product. From its connections to Lyapunov exponents to its more algebraic nature, the drift finds multiple applications which makes its study interesting. Our goal in this topic is to study the continuity of the drift, and discuss the implications of curvature in this study.