Phase separation and extreme sensitivity to disorder and defects are key features of electronic order near quantum phase transitions. Neutron depolarization imaging and neutron Larmor diffraction are new experimental techniques capable of providing detailed real-space and reciprocal-space information, respectively, on the existence and nature of phase separations. Proof-of-principle depolarization imaging in Pd _1-x Ni _x, CePd _1-x Rh _x and NbFe ₂ suggests distinct differences of the real-space distribution of ferromagnetic moments and Curie temperatures in materials at ferromagnetic quantum phase transitions. This compares with neutron Larmor diffraction which provides high-resolution reciprocal-space information of phase separation and the absence of quantum criticality in the itinerant helimagnet MnSi or the parasitic nature of small moment antiferromagnetism in URu ₂Si ₂.