Realizing experimentally continuous phase transitions in the electronic ground state of materials near zero temperature as a function of tuning some external parameter (magnetic field, pressure etc.) offers a unique opportunity to probe the extreme regime (near the transition point) where strong quantum correlations encompass the macroscopic sample as a whole, so called “quantum criticality” . In this regime of strong correlations small perturbations/interactions can stabilize novel forms order or collective fluctuations that otherwise do not exist. One of the theoretically most studied paradigms for quantum criticality is a chain of Ising spins driven by a transverse field to a critical point separating spontaneous magnetic order and paramagnetic phases. We have realized this system experimentally by applying strong magnetic fields to the quasi-one-dimensional Ising ferromagnet CoNb2O6 and have probed via single-crystal inelastic neutron scattering the evolution of the magnetic order and spin excitation spectrum as a function of applied field at mili-Kelvin temperatures . Near the critical point the spin excitations were theoretically predicted nearly two decades ago to have a set of quantum resonances (collective modes of vibration of the interacting spins) with universal ratios between their frequencies reflecting an exceptional mathematical structure of the quantum many-body eigenstates with a “hidden” E8 symmetry governing the physics in the scaling limit. Experiments indeed observed evidence for a spectrum of resonances and the ratio between the frequencies of the two lowest modes approached the "golden ratio" near the critical point, as predicted by field theory. As a second example of novel physics near quantum criticality I will discuss how an amplitude-modulated incommensurate spin-density wave (SDW) order appears near the field-induced critical point in the quasi-1D spin-1/2 XY antiferromagnet Cs2CoCl4. Incommensurate SDWs are very uncommon in magnetic insulators and are not stable zero-temperature ground states at the classical mean-field level, we propose that here such a state is stabilized by the strong quantum fluctuations associated with the proximity to the critical point and the weak frustrated inter-chain couplings.