Frustrated antiferromagnets are a very rich class of physical systems, in which various new phases of matter are expected to be realized. From a theoretical point of view, however, they present challenging difficulties and typically defy a full quantum treatment. A possible strategy is to restrict oneself to a specific region of the parameter space, namely the one of high applied magnetic field, where the problem can be mapped to a dilute Bose gas of magnons. In this way we can provide benchmarks for the latest numerical approaches, such as in the case of the prototypical spin-1/2 XXZ model on the triangular lattice [1]. In more complicated models with competing exchange interactions, we find new types of magnetic order, such as a double-q state with striped chiral order [2]. Several problems remain open in this field-theoretical approach, in particular three-magnon and four-magnon scattering amplitudes, which relate to a recently discovered magnetic "0-pi" phase transition and to the stability of the spin nematic phase respectively.

[1] D. Yamamoto, G. Marmorini and I. Danshita, Phys. Rev. Lett. 112
(2014) 127203.
[2] G. Marmorini and T. Momoi, Phys. Rev. B 89, 134425 (2014).