We survey recent results on the constructive approximation
of the distribution of the solution of an SDE by probability
measures with finite support, i.e., by quadrature formulas
with positive weights summing up to one.
Here we either consider the distribution on the path
space or a marginal distribution on the state space.
We provide asymptotic results on the $N$-th minimal error of
deterministic and randomized algorithms,
which is the smallest
error that can be achieved by any such algorithm
not exceeding the cost bound $N$.
Joint work with
Steffen Dereich (Marburg),
Thomas M\'uller-Gronbach (Passau),
Reik Schottstedt (TU Berlin),
Larisa Yaroslavtseva (Passau).