This talk is mainly about a new Minkowski formula for  hypersurfaces with free boundary or capillary boundary supported on the unit sphere. With it we have classified all stable free boundary CMC hypersurfaces.  Using it we have introduced a inverse curvature flow, which is used to prove Alexandrov-Fenchel type inequalities for newly introduced quermassintegrals  for free boundary  hypersurfaces. At the end we will talk about various generalizations. The talk is based on the joint work with J. Scheuer and C. Xia and other collaborators.