  The glass transition of supercooled fluids is a particular challenge for
computer simulation, because the (longest) relaxation times increase by about
15 decades upon approaching the transition temperature T_g. Brute-force
molecular dynamics simulations, as presented here for molten SiO_2 and
coarse-grained bead-spring models of polymer chains, can yield very useful
insight about the first few decades of this slowing down. Hence this allows to
access the temperature range around T_c of the so-called mode coupling theory,
whereas the dynamics around the experimental glass transition is completely out
of reach. While methods such as ``parallel tempering'' improve the situation
somewhat, a method that allows to span a significant part of the region T_g\leq
T\leq T_c is still lacking. Only for abstract models such as the infinite range
10-state Potts glass with a few hundred spins this region can be explored.
However this model suffers from very strong finite size effects thus making it
difficult to extrapolate the results obtained for the finite system sizes to
the thermodynamic limit. For the case of polymer melts, two different
strategies to use lattice models instead of continuum models are discussed: In
the first approach, a mapping of an atomistically realistic model of
polyethylene to the bond fluctuation model with suitable effective potentials
and a temperature-dependent time rescaling factor is attempted. In the second
approach, devoted to a test of the entropy theory, moves that are artificial
but which lead to a faster relaxation (``slithering snake'' algorithm) are
used, to get at least static properties at somewhat lower temperatures than
possible with a ``realistic'' dynamics. The merits and shortcomings of all
these approaches are discussed.
