This monograph, together with its accompanying first part Cattaneo, Idrobo and Titiunik (2020), collects and expands the instructional materials we prepared for more than $50$ short courses and workshops on Regression Discontinuity (RD) methodology that we taught between 2014 and 2023. In this second monograph, we discuss several topics in RD methodology that build on and extend the analysis of RD designs introduced in Cattaneo, Idrobo and Titiunik (2020). Our first goal is to present an alternative RD conceptual framework based on local randomization ideas. This methodological approach can be useful in RD designs with discretely-valued scores, and can also be used more broadly as a complement to the continuity-based approach in other settings. Then, employing both continuity-based and local randomization approaches, we extend the canonical Sharp RD design in multiple directions: fuzzy RD designs, RD designs with discrete scores, and multi-dimensional RD designs. The goal of our two-part monograph is purposely practical and hence we focus on the empirical analysis of RD designs.