Abstract
When heated and/or compressed, strongly interacting matter exhibits a rich phase structure. In this talk, I will concentrate on its behavior under variations of the temperature, which is most relevant for phenomenological applications such as in cosmology, heavy-ion collisions, and astrophysics.In particular, effective field theory methods can be used to combine lattice and continuum calculations, in order to obtain high-precision results for the relevant thermodynamic quantities such as the QCD pressure and equation of state. I will discuss the current status of this systematic approach to QCD thermodynamics, and point out the remaining (technical) problems.
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