  In this PhD thesis, I will review recent progress in perturbative studies of
energy momentum tensor correlators in high-temperature Yang-Mills theory. After
briefly introducing the necessary tools and physical motivation, I proceed to
discuss the machinery developed for the extraction of next-to-leading order
Operator Product Expansions and thermal spectral functions and to introduce the
results obtained in the bulk and shear channels of Yang-Mills theory.
Particular emphasis is placed on the comparison of the results with recent
lattice and gauge/gravity calculations, as well as on discussing their use in
extracting the corresponding transport coefficients from Euclidean lattice
data.
