  The dynamical (super)symmetries for various monopole systems are reviewed.
For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however,
a spectrum-generating conformal $o(2,1)$ dynamical symmetry that extends into
$osp(1/1)$ or $osp(1/2)$ for spin 1/2 particles. Self-dual 't
Hooft-Polyakov-type monopoles admit an $su(2/2)$ dynamical supersymmetry
algebra, which allows us to reduce the fluctuation equation to the spin zero
case. For large $r$ the system reduces to a Dirac monopole plus an suitable
inverse-square potential considered before by McIntosh and Cisneros, and by
Zwanziger in the spin 0 case, and to the `dyon' of D'Hoker and Vinet for spin
1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a
`helicity-supersymmetry' analogous to the one Biedenharn found in the
relativistic Kepler problem. Similar results hold for the Kaluza-Klein monopole
of Gross-Perry-Sorkin. For the magnetic vortex, the N=2 supersymmetry of the
Pauli Hamiltonian in a static magnetic field in the plane combines with the
$o(2)\times o(2,1)$ bosonic symmetry into an $o(2)\times osp(1/2)$ dynamical
superalgebra.
