  This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and
their mutual relations. The Hopf maps of division algebras provide a prototype
relation between monopoles and fuzzy spheres. Generalization of complex numbers
to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres
to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an
interesting hierarchical structure made of "compounds" of lower dimensional
spheres. We give a physical interpretation for such particular structure of
fuzzy spheres by utilizing Landau models in generic even dimensions. With
Grassmann algebra, we also introduce a graded version of the Hopf map, and
discuss its relation to fuzzy supersphere in context of supersymmetric Landau
model.
