A Riemannian foliation is a foliation whose normal bundle admits a holonomy invariant Riemannian metric. In this talk, we would discuss the notion of transverse Lie algebra actions on Riemannian foliations, which is used as a model for Lie algebra actions on the leave spaces. Using an equivariant version of the basic cohomology theory on Riemannian foliations, we explain that when the action preserves the transverse Riemannian metric, there is a foliated version of the classical Borel-Atiyah-Segal localization theorem. Using the transverse integration theory for basic forms on Riemannian foliations, we would also explain how to establish a foliated version of the Atiyah-Bott-Berline-Vergne integration formula, which reduces the integral of an equivariant basic cohomology class to an integral over the set of invariant leaves. This talk is based on a joint work with Reyer Sjamaar.