  We give an overview of recent work on charge degrees of freedom of strongly
correlated electrons on geometrically frustrated lattices. Special attention is
paid to the checkerboard lattice, i.e., the two-dimensional version of a
pyrochlore lattice and to the kagome lattice. For the checkerboard lattice it
is shown that at half filling when spin degrees of freedom are neglected and
quarter filling when they are included excitations with fractional charges
$\pm$e/2 may exist. The same holds true for the three-dimensional pyrochlore
lattice. In the former case the fractional charges are confined. The origin of
the weak constant confining force is discussed and some similarities to quarks
and to string theory are pointed out. For the checkerboard lattice a
formulation in terms of a compact U(1) gauge theory is described. Furthermore a
new kinetic mechanism for ferromagnetism at special fillings of a kagome
lattice is discussed.
