This research review 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. The prominent articles discussed in this review are written by leading scholars and break new ground, providing definitive statements of the current best practices in those respective areas. It describes 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.