Gaussian generation-recombination is accepted to be a dominant mechanism of current noise source in quantum well systems biased by electric field normal to the layers. Recent experiments in n-type and p-type multiple quantum wells have revealed an additional pronouncedly non-Gaussian excess current noise with a low cut-off frequency in the kHz range. The non-Gaussian noise has been attributed to metastable spatial configurations of electric field. The metastability is originating from negative differential conductance caused by intervalley scattering in n-type wells and heavy and light holes tunneling in p-type wells. At a constant bias the system randomly switches between high resistivity state with low current flow and low resistive state with high current. The non-Gaussianity of the noise is more pronounced in p-type wells where the time traces of current fluctuations resemble closely two-level random telegraph signal. In n-type wells the telegraph-like fluctuations have not been straightforwardly observed. The non-Gaussianity of the noise in n-type systems has been revealed by nonzero skewness. The differences between noise properties of between n- and p-type systems have been attributed to small capture probability of electrons in n-type wells, as opposed to very high capture probability of holes in p-type wells. As a consequence the noise of any p-type multi-well system is dominated by the tunneling from the wells while in the n-type the noise appears as a superposition of many fluctuators associated with individual wells.