Understanding the ionizing spectrum of low-metallicity galaxies is of great importance for modeling and interpreting emission line observations of early/distant galaxies. Although a wide suite of stellar evolution, atmosphere, population synthesis, and photoionization models, taking many physical processes into account now exist, all models face a common problem: the inability to explain the presence of nebular HeII emission, which is observed in many low metallicity galaxies, both in UV and optical spectra. Several possible explanations have been proposed in the literature, including Wolf-Rayet (WR) stars, binaries, very massive stars, X-ray sources, or shocks. However, none has so far been able to explain the major observations. We briefly discuss the HeII problem, available empirical data, and observed trends combining X-ray, optical and other studies. We present a simple and consistent physical model showing that X-ray binaries could explain the long-standing nebular HeII problem. Our model, described in Schaerer et al. (2019), successfully explains the observed trends and strength of nebular HeII emission in large samples of low metallicity galaxies and in individual galaxies, which have been studied in detail and with multi-wavelength observations. Our results have in particular important implications for the interpretation of galaxy spectra in the early Universe, which will be obtained with upcoming and future facilities.
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