Post-rift, deep water stratigraphic traps, the main theme of this presentation, have proven highly material where they have a large connected reservoir pore volume and are associated with a rich, active petroleum system. Significant discoveries of this type include the Marlim, Roncador, Albacora, and Mexilhao fields from offshore Brazil, the Foinhaven and Schiehallion fields from the West Shetland Basin, and Ceiba, Jubilee, Tweneboa and Enyenra from offshore West Africa. Similar subtle traps are also a common success theme in syn- and post-rift stratigraphy of intracratonic rift basins such as the North Sea and likely occur in other underexplored rift, sag and post-rift basins globally. In other areas, however, successful traps have proven to be less than commercial in size. This contribution will present observations on the trapping styles that are commonly encountered. These include global statistics on field size and geographic distribution; the seismic technology used to help identify these; the statistics behind these discoveries; and from these identify some of the pitfalls and challenges awaiting those eager to join the hunt but for whom geology or serendipity do not favor.