  We give a detailed critical discussion of the properties of Wilsonian
effective actions, defined by integrating out all modes above a given scale
$\mu$. In particular, we provide a precise and relatively convenient
prescription how to implement the infrared cutoff $\mu$ in any loop integral
that is manifestly Lorentz invariant and also preserves global linear
symmetries such as e.g. supersymmetry. We discuss the issue of gauge invariance
of effective actions in general and in particular when using background field
gauge. Our prescription for the IR cutoff (as any such prescription) breaks the
gauge symmetry. Using our prescription, we have explicitly computed, at one
loop, many terms of the Wilsonian effective action for general gauge theories,
involving bosonic and fermionic matter fields of arbitrary masses and in
arbitrary representations, exhibiting the non-gauge invariant (as well as the
gauge invariant) terms. However, for supersymmetric gauge theories all
non-gauge invariant terms cancel within each supermultiplet. This is strong
evidence that in supersymmetric gauge theories this indeed defines a Lorentz,
susy and gauge invariant Wilsonian effective action. As a byproduct, we obtain
the explicit one-loop Wilsonian couplings for all higher-derivative terms $F
D^{2n}F$ in the effective action of arbitrary supersymmetric gauge theories.
