We investigate the variation of galaxy clustering with luminosity using the recently completed SSRS2 sample. Clustering measurements based on the two-point correlation function and the variance of counts in cells reveal a strong dependence of clustering on luminosity for galaxies brighter than L*, while no significant variation is detected for fainter galaxies. We derive a relative bias versus magnitude relation that can be compared with theoretical predictions. Existing models of galaxy formation cannot reproduce adequately the simultaneous steep rise of biasing at high luminosities and the plateau at the low-luminosity end. Improved modeling of halo-galaxy relation and larger samples including low-luminosity galaxies are required to draw more definitive conclusions.