  We discuss the concepts of fine and coarse moduli spaces in the context of
finite dimensional algebras over algebraically closed fields. In particular,
our formulation of a moduli problem and its potential strong or weak solution
is adapted to classification problems arising in the representation theory of
such algebras. We then outline and illustrate a dichotomy of strategies for
concrete applications of these ideas. One method is based on the classical
affine variety of representations of fixed dimension, the other on a projective
variety parametrizing the same isomorphism classes of modules. We state sample
results and give numerous examples to exhibit pros and cons of the two lines of
approach. The juxtaposition highlights differences in techniques and attainable
goals.
