Currently, although the global population has surpassed 7.5 billion and continues to increase in about 80 million each year, attention to demography is almost absent in most of the studies and publications related to the current situation of planetary emergency and the necessary transition to sustainable societies. For this reason, our first aim in this paper has been to discuss if this current lack of attention to demography is justified or not. With this purpose, we begin considering the scientific meaning of Sustainability, in order to overlay distorted and impoverish views of this concept that may hinder our study. Then, we analyse the reasons given by experts for and against the incidence of demographic growth in the current unsustainable situation of planetary emergency. Finally, we present proposals to face the ensemble of interconnected socio-environmental problems (including demographic evolution), to make possible an appropriate transition to sustainable societies.