This review provides an introduction to the geodynamic processes that influence tectonic rift evolution and rifted margin architecture. With a strong focus on numerical modeling, I summarize classical and recent insights on rift evolution with differentiation between 2D and 3D concepts and models. One of the key processes during rift evolution is crust-mantle coupling, which controls not only the width of a rift system but also crustal hyperextension and the degree of final margin asymmetry. Accounting for 3D rift geometries allows investigating along-strike heterogeneities, rift segmentation and rift obliquity. Large amounts of sediments have accumulated at rifted margins, especially at the mouths of large rivers and former glaciers, providing important stratigraphic archives and georesources. Shifting the focus from the geological scale of continental extension to the human time scale, natural hazards are discussed regarding earthquakes and volcanic eruptions during active rifting. Finally, I review natural hazards due to passive margin seismicity as well as slope instabilities at heavily sedimented continental margins that have the potential to generate large landslide tsunamis.