Recent advances on the quest to determine the primordial or pregalactic helium abundance, Yp, are reviewed. There are seven problems affecting the He/H abundance determinations of H II regions that are briefly discussed: the underlying absorption lines in the observed spectra, the ionization, temperature, and density structures of each object, the collisional contribution to the intensity of the He I and H I lines, the optical thickness of the He I lines, and the extrapolation to derive Yp based on the Y and O/H values.