Quantum magnets in insulating structures have proven to be remarkable systems

when subjected to a strong magnetic field.
In addition to their own intrinsic interest they can be mapped on model systems

of itinerant quantum particles. This has allowed to use them as quantum simulators

for studying the properties of interacting hard core bosons.

In particular I will focus on two recent ladder compounds for which a
combination of numerical studies and analytical ones has allowed to obtain fully

the dynamical correlation functions.
I will review the recent results in that respect, in particular some of the experiments

and the corresponding theories for phenomena such as Bose-Einstein condensation and

Tomonaga-Luttinger liquids as observed by neutrons, NMR and also ESR.
I will discuss the recent successes in this domain as well as several of the open

problems and perspectives offered by such compounds such as the possibility to study dimensional crossover, disorder effects etc.