AdS/CFT Correspondence
Strongly interacting systems (SIS) are very common in Nature, famous examples ranging from the fundamental theory of quarks and gluons  Quantum ChromoDynamics (QCD)  to quantum critical systems, hightemperature superconductors, strange metals, quantum Hall systems and possibly even new materials as graphene. In these systems the interaction between different particles becomes so intense that the most common mathematical tools used to describe them break down and the traditional paradigms based on weakly interacting degrees of freedom cannot be applied.
A promising powerful technique to investigate SIS is the holographic correspondence, often referred to as AdS/CFT or gauge/gravity duality. It is founded on a duality map between ordinary quantum field theories (QFTs) and higher dimensional models of gravity and strings. 
Remarkably, this allows suitably defined regimes, where the underlying QFT is strongly interacting, to be described by means of a classical, weakly coupled, model. Typically the dual theory contains gravity and extended objects, like fundamental strings and DBranes. In this way, hardly solvable quantum problems are mapped into easier, although nonlinear, classical ones in the dual description. The AdS/CFT correspondence offers a concrete possibility to go beyond the perturbative regime and to understand the underlying structures of strongly coupled gauge theories.
Useful Reviews: arXiv:hepth/9905111 (Old, but classic Review on the subject), arXiv:hepth/0201253 (Another classical review), arXiv:0712.0689 (A complete set of lectures on AdS/CFT correspondence. Se also the book) Scientific American paper by J. Maldacena (A general introduction to the topic)
Localisation and Integrability
The growing activity around the AdS/CFT paradigm has fostered the development of new techniques, mainly in the context of supersymmetric QFTs, to understand exact dynamics of quantum gauge theories.
Localization is one of these: the supersymmetry algebras can be sometimes deformed to accommodate background curvatures and the partition functions for the resulting quantum theories can be evaluated in closed form via a particular saddlepoint procedure, known as the supersymmetric localization. Thanks to this method, a huge number of new exact results has been derived in different contexts, for local and nonlocal 
observables: the strong coupling limits have been compared with holography prediction, supporting in general the validity of the duality.
The duality has also benefited from all the tools provided by integrability. The latter is a fundamental ingredient for understanding the gravitational/string description of certain strongly interacting gauge theories. For instance, the sigmamodels effectively describing their strong coupling regime are in some cases naturally endowed with an integrable structure. Quite surprisingly this property survives in the dual field theoretical picture and is used to obtain exact results at any coupling for quantities such as the spectrum of anomalous dimensions of operators in maximally supersymmetric QFTs!
Lately the correspondence has also led to unravel novel relations between observables, such as the connection between scattering amplitudes and Wilson loops superconformal gauge theories. 
People workings on this topics here: D. Seminara
Useful Reviews: Localisation, arXiv:1502.04543 (A review on the many results obtained through this technique), arXiv:1412.7134 (A technical introduction on localisation in N=2 theories, three video lectures by the same author can be find here), arXiv:1104.0783 (A very nice introduction to the D=3 results). A long review on many features concerning localisation has recently appeared and it can be found at the following http URL
Integrability, arXiv:1012.3982 (the initial link to a megareview written by many different authors, 550 pages where you find almost everything you want to know), arXiv:hepth/0407277 (Ph.D. thesis of N. Beisert a cornerstone in the field), arXiv:hepth/0507136 (A short and readable introduction to the subject).
Useful Reviews: Localisation, arXiv:1502.04543 (A review on the many results obtained through this technique), arXiv:1412.7134 (A technical introduction on localisation in N=2 theories, three video lectures by the same author can be find here), arXiv:1104.0783 (A very nice introduction to the D=3 results). A long review on many features concerning localisation has recently appeared and it can be found at the following http URL
Integrability, arXiv:1012.3982 (the initial link to a megareview written by many different authors, 550 pages where you find almost everything you want to know), arXiv:hepth/0407277 (Ph.D. thesis of N. Beisert a cornerstone in the field), arXiv:hepth/0507136 (A short and readable introduction to the subject).
AdS/QCD
A typical problem one can address in this framework is the strong dynamics of hadronic matter. A firstprinciple approach is provided by a reformulation of QCD on Euclidean lattices and the use of numerical Monte Carlo methods. This technique, powerful when studying equilibrium properties, has still severe limitations when analyzing realtime dynamical issues or finite quark density regimes. Holography has already had some success in modelling the low viscosity fluid state of matter called Quark Gluon Plasma, which was created in heavy ion collision experiments at Brookhaven National Laboratory, and, more recently, at the LHC at CERN. Moreover in QFT models where additional symmetries are present (typically supersymmetries) exact dynamical properties of the strong coupling regime as confinement, chiral symmetry breaking and critical exponents have been derived by using gauge/gravity duality.
People working on this topics here: F. Bigazzi, A. Cotrone and D. Seminara Useful Reviews: arXiv:0709.1523 (A simple and classic review by D. Mateos). see also the book by J. Erdmenger 
AdS/CMT
Other paradigmatic examples, of high technological relevance, arise in the application of these techniques to condensed matter systems in 2 and 3 spatial dimensions, in particular to systems exhibiting quantum critical behavior. Quantum critical systems, superconductors with a high critical temperature, ultracold Fermi gases at unitarity, quantum Hall systems, strange metals, graphene, all appear to evade most of the traditional paradigms (e.g. LandauFermi liquid or BCS theories) based on sharp quasiparticles or weakly coupled degrees of freedom. It is thus extremely urgent to develop novel theoretical frameworks where these systems can be modeled and analyzed.
People working on this topics here: F. Bigazzi, A. Cotrone and D. Seminara Useful Reviews: An interesting set of lectures, arXiv:0909.0518 (Very good introductory lectures) 
Non equilibrium quantum systems

Attention has been recently focused on (generalized) thermalization mechanisms in onedimensional quantum systems and on outofequilibrium transport properties.
Concerning transport properties in a nonequilibrium stationarystate (NESS), a very interesting situation is obtained by considering a gas of atoms initially split into two different packets, each of them prepared at given initial temperature. The gas is then released and left to evolve freely. Nonequilibrium dynamic is starting to be studied also in high energy physics (e.g. in the context of the AdS/CFT correspondence). With respect to thermalization, if we consider non integrable quantum systems the stationary behavior can be described by a thermal state (Gibbs ensemble). 
For integrable systems the picture changes drastically: the number of local conserved charges is infinite and the obvious generalization is to construct an ensemble that contains all infinite conserved quantities. The idea is that the equilibrium is local and they define the Generalized Gibbs Ensemble (GGE) considering only the local conserved charges. Recently it was observed that the GGE conjecture fails in its original form in the case of interacting integrable field theories possessing string eigenstates. The Quench Action Method predicts the correct behavior of the relaxation dynamic instead of the GGE, but without information about the role of the conserved charges.
People working on this topics here: G. Martelloni
Useful Reviews: A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011) (non equilibrium); http://arxiv.org/abs/1603.04689 (QAM); http://arxiv.org/abs/1603.07765 (NESS).
People working on this topics here: G. Martelloni
Useful Reviews: A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011) (non equilibrium); http://arxiv.org/abs/1603.04689 (QAM); http://arxiv.org/abs/1603.07765 (NESS).