  We review a number of topics related to block variable renormalisation group
transformations of quantum fields on the lattice, and to the emerging perfect
lattice actions. We first illustrate this procedure by considering scalar
fields. Then we proceed to lattice fermions, where we discuss perfect actions
for free fields, for the Gross-Neveu model and for a supersymmetric spin model.
We also consider the extension to perfect lattice perturbation theory, in
particular regarding the axial anomaly and the quark gluon vertex function.
Next we deal with properties and applications of truncated perfect fermions,
and their chiral correction by means of the overlap formula. This yields a
formulation of lattice fermions, which combines exact chiral symmetry with an
optimisation of further essential properties. We summarise simulation results
for these so-called overlap-hypercube fermions in the two-flavour Schwinger
model and in quenched QCD. In the latter framework we establish a link to
Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In
particular we present an evaluation of the leading Low Energy Constants of the
chiral Lagrangian - the chiral condensate and the pion decay constant - from
QCD simulations with extremely light quarks.
