Abstract: In recent years, an online adaptation of the classical primal-dual paradigm has been successfully used to obtain new online algorithms for node-weighted network design problems, and simplify existing ones for their edge-weighted counterparts. In this talk, I will give an outline of this emerging toolbox using three fundamental problems in this category for illustration: the Steiner tree problem (Naor-P.-Singh, 2011), the Steiner forest problem (Hajiaghayi-Liaghat- P., 2013), and their respective prize-collecting variants (Hajiaghayi-Liaghat-P., 2014).