In the present paper we survey the most recent classification results for
proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some
new results concerning geometric properties of proper biharmonic constant mean
curvature submanifolds in spheres.Comment: 10 pages; contribution to the Proceedings of the 11-th International
Conference on Geometry, Integrability and Quantization, Varna 2009, Bulgari
