This paper will look at the existing gaps in the research of the 6^th and 5^th mill. BC, the time span including Late Neolthic and Chalcolithic research. Gaps are understood here in a regional/geographical meaning to indicate, which areas are underresearched and which areas might have -in the moment- been studied quite thoroughly (there is never too much study!). But it means also gaps concerning particular aspects of research, such as village versus town, or cultic architecture versus domestic architecture, or stratigraphy versus social organisation (these pairs are not necessarily excluding each other). Problems in the research are continuing in some topic such as our understanding of chronology and regional diversification. Promises on the other hand are just meant to point into possibly fruitful directions in Late Neolithic and Chalcolithic studies, where future research will bring us forward in solving poblems and closing gaps. This lecture is not intending to solve any questions, but more to raise new ones and indicate possible gateways to future answers.