The last centuries have seen a great surge in our understanding and control of ‘simple’ physical, chemical, and biological processes through data analysis and the mathematical modelling of their underlying dynamics. Encouraged by its success, researchers have recently embarked on extending such approaches to gain qualitative and quantitative understanding of social and economic systems and the dynamics in and of them. This has become possible due to the massive amounts of data generated by information-communication technologies and the unprecedented fusion of off- and on-line human activity. However, due to the presence of adaptability, feedback loops, and strong heterogeneities of the individuals and interactions making up our modern digital societies, it is yet unclear if statistical ‘laws’ of socio-technical behaviour even exist, akin to those found for natural processes. Such continuing search has resulted in the fields of computational social science and social network science, which share the goal of first analysing social phenomena and then modelling them with enough accuracy to make reliable predictions. This Special Issue invites contributions to such fields of study, with focus on the temporal evolution and dynamics of complex social systems. As topics of interest, we propose research on more realistic models of social dynamics, the use of statistical inference, machine learning, and other cross-disciplinary techniques to complement the analysis of social dynamics, and the creation of loops between data acquisition and model analysis to increase accuracy in the prediction of social trends. We hope this Special Issue will bring together expertise from a wide range of research communities interested in similar topics, including computational social science, network science, information science, and complexity science.