This research collection offers a 34-article tour of recent advances and the current state of 5 important and booming areas of empirical methodology: Bayesian methods; modelling of temporal duration, dependence, and dynamics; network-analytic methodology; text, classification, and big-data analytic methods; methods for nonparametric and design-based causal inference. These prominent articles, written by leading scholars, break new ground and provide definitive statements of the current best practices in those respective areas. Together they describe the cutting-edge profile of modern empirical methodology for applied empirical analysis in political science. This is an essential resource for those studying and researching political methodology.