The article considers the evolution of two “Second Demographic Tradition” (SDT) core characteristics: fertility postponement and the rise of cohabitation, with particular attention being given to the first two decades of the new century. It can be considered as the sequel to the concise overview of the SDT published earlier in the US Proceedings of the National Academy (PNAS) (Lesthaeghe, 2014).In the first section, three optimistic views concerning the evolution of fertility are considered: (i) rises due to the end of postponement, (ii) rises connected with advancing human development and (iii) rises associated with advancing gender equality. The focus in this section is mainly but not exclusively on the European experience and its large degree of variation in fertility patterns. It is argued that these three optimistic predictions of sustained fertility rises are mainly based on observations prior to 2010, with too much weight being given to four Nordic countries and too little to other Western European countries with very similar fertility levels. However, these expectations have been thwarted during the second decade, even in the presence of advances in human development and/or gender equality. Hence, the original SDT prediction of 1986 of sustained sub-replacement fertility still holds after 35 years. We expect this to continue during the third decade as well. Furthermore, single-factor explanations are not likely to do justice to far more intricate situations that are responsive to varying structural and ideational influences.In the second section, the evolution of cohabitation is traced in Europe, the USA and Canada, the Latin American countries, three East Asian populations and selected sub-Saharan cases. At the onset, cohabitation can start either from a SDT basis among the better educated or among the poorer classes following a pattern of disadvantage (POD). It is argued that the feature of cohabitation spreads rapidly among all social classes and across all education groups and that in the process of increasing cohabitation, the POD versus SDT argument loses its significance. On a global scale, the rise in cohabitation is contingent on two dimensions: (i) contrasting historical patterns of kinship organisation, including the position of women, and (ii) further advances of the “ethics revolution”, indicating the growing dominance of individual autonomy over traditional societal norms. As a result, no breakthroughs in the near future are expected in countries with a Muslim or Hindu tradition in which no such major cultural shifts have occurred so far.