This talk concerns $L^p$ bounds on the strong spherical maximal functions that are multi-parametric maximal functions defined by averages over ellipsoids. We obtain $L^p$ bounds on those maximal operators for a certain range of nontrivial p. No such maximal bounds have been known until recently. In particular, our results extend Stein’s celebrated spherical maximal bounds to multi-parametric versions. The talk is based on joint work with Juyoung Lee and Sewook Oh.