3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of detailed shapes. This report surveys different approaches of shape modeling and correspondence especially for shapes exhibiting topological complexity. We focus on methods designed to help generate or process shapes with large number of interconnected components often found in man-made shapes. We first discuss a variety of modeling techniques, that leverage existing shapes, in easy to use creative modeling systems. We then discuss possible correspondence strategies for topologically different shapes as it is a requirement for such systems. Finally, we look at different shape representations and tools that facilitate the modification of shape topology and we focus on those particularly useful in free-form 3D modeling.