Nebular HeII1640,4686 emission, observed to be more frequent in high-z galaxies than locally, is indicative of far harder ionizing spectrum than that seen in nearby systems. Star-forming galaxies with lower metal content tend to have a larger nebular HeII intensities compared to those with higher metallicities. This agrees with the expected harder spectral energy distribution at the lower metallicities typical in the early universe. Theoretical arguments suggest that Pop III stars have spectra hard enough to produce many HeII-ionizing photons; the high-ionization HeII line is considered to be one of the best signatures to single out candidates for PopIII-host galaxies. But, despite various attempts to explain the formation of nebular HeII emission, its origin remains mysterious in many cases both at high and low redshifts. Before interpreting high-z HeII-emitters, it is crucial to understand HeII ionization nearby. I will give examples of what we can learn studying nearby, metal-poor HeII-emitting galaxies by spatially resolving them.