Study of strong interactions I've been learning that quantum field theories are essentially perturbative approaches towards interacting phenomena, which makes them very useful to study weakly interacting particles like in QED. However, since QCD deals mostly with strong interactions, the perturbations don't converge and its applications aren't as useful as in QED.
So far I know of two approaches: lattice QCD (where we discretize space-time) and AdS/CFT (where we can study non-perturbative phenomena through a holographic "mapping" in a theory we can work out more easily). However, I was curious if there were other good approaches to study these kind of strong phenomena, such as quark-gluon plasma.
 A: Well, I would say it is a bit of a misconception that perturbation theory is not applicable in QCD. Actually, a lot of people actually do employ perturbative QCD, the reason being that the strong coupling constant is a function of the scale (which could be, for instance, the exchanged four-momentum in the collision, or the mass of a heavy particle that is produced), and becomes smaller than one for scales in the ballpark of 1 GeV (see the plot fro the particle data group). The fun is then in trying to separate what you can calculate in perturbation theory, called the 'hard' part, from all those things which have to do with nonperturbative physics, and this idea is called factorization. A simple example would be the cross section for deep-inelastic scattering, in which an electron scatters off a proton, breaking the latter up in the process, which can be written as the perturbative electron-quark interaction (via a photon) on the one hand, and the nonperturbative 'parton distribution function' (PDF) on the other hand which encodes the way the quarks (or gluons) are distributed inside the proton. The latter then needs to be extracted from experiments.
For the purely nonperturbative sector of QCD, apart from lattice QCD, holography and the Schwinger-Dyson equations, as David Schaich commented, there is also Regge theory which should be mentioned. Regge theory cannot really be called QCD (it doesn't involve a Lagrangian) but rather relies on the unitarity and analyticity of the S-matrix, and is from the sixties until now widely used to describe strong interaction physics at low energies.
Finally, the quark-gluon plasma might very well be strongly coupled indeed, hence as such perturbation theory seems completely useless. People mainly use relativistic hydrodynamics to study its global properties.  However, again perturbative QCD can be used to describe at least aspects of the QGP. For instance, the nuclei just before and right after a heavy ion collision are commonly described in the Color Glass Condensate (CGC). The CGC is an effective theory of QCD, which describes gluons in a very high-density regime (such as a boosted nucleus). Although this regime is strictly speaking non-perturbative, due to the high density of gluon fields, it can be described with weak-coupling techniques due to an intrinsic perturbative scale, the 'saturation scale', which appears due to the nonlinear interactions of the gluons. 
Second, an energetic particle, produced in the collision of the nuclei, has to travel through the quark-gluon plasma to reach the detector. Even though the QGP is strongly coupled, the interaction of the particle with the plasma is not, at least if the particle's energy is large enough. This interaction gives rise to a lot of phenomena (broadening of the transverse momentum of the particle, energy loss through induced gluon radiation,...) called 'jet quenching', which are very commonly studied using perturbation theory, again because the coupling of the particle/jet with the plasma's constituents is weak enough.
Hope this helps!

