In this talk, we will give a brief introduction of isoparametric foliation in real space forms. Then we survey our results on the geometry of isoparametric foliation, including affirmative answer to the Yau conjecture on the first eigenvalue in the isoparametric case, negative answer to Yau's 76th problem，Besse's problem on generalizations of Einstein conditions, Normal scalar curvature inequalities on focal submanifolds and a sufficient condition for a hypersurface to be isoparametric.
