  This paper is a slightly modified version of the introductory part of a
doctoral dissertation also containing the articles hep-ph/0311268,
hep-ph/0510375, hep-ph/0512177 and hep-ph/0701250. The thesis discusses
effective field theory methods, in particular dimensional reduction, in the
context of finite temperature field theory. We first briefly review the
formalism of thermal field theory and show how dimensional reduction emerges as
the high-temperature limit for static quantities. Then we apply dimensional
reduction to two distinct problems, the pressure of electroweak theory and the
screening masses of mesonic operators in hot QCD, and point out the
similarities. We summarize the results and discuss their validity, while
leaving all details to original research articles.
