Abstract: The dynamics of M-dimensional extended objects arising from stationary points of the world volume swept out in space time is discussed from various points of view. An introduction to the Hamiltonian mechanics of bosonic compact M(em)branes is given, emphasizing the diversity of the different formulations. For moving hypersurfaces, a graph description—including its nonlinear realization of Lorentz invariance—and hydrodynamic formulations are presented. A matrix regularization for M = 2 (existing for all topologies) is explained in detail. The recently found dynamical symmetry that exists for all M will briefly be explained.