  The causal approach to perturbative quantum field theory is presented in
detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko
Glaser in 1973. Causal perturbation theory is a mathematically rigorous
approach to renormalization theory, which makes it possible to put the
theoretical setup of perturbative quantum field theory on a sound mathematical
basis. Epstein and Glaser solved this problem for a special class of
distributions, the time-ordered products, that fulfill a causality condition,
which itself is a basic requirement in axiomatic quantum field theory. In their
original work, Epstein and Glaser studied only theories involving scalar
particles. In this review, the extension of the method to theories with higher
spin, including gravity, is presented. Furthermore, specific examples are
presented in order to highlight the technical differences between the causal
method and other regularization methods, like, e.g. dimensional regularization.
