A fundamental understanding of droplet dynamics is important for the prediction and optimization of technical systems involving drops and sprays. The Collaborative Research Center (CRC) SFB-TRR 75 was established in January 2010 to focus on the dynamics of basic drop processes, and in particular on processes involving extreme boundary conditions, for example near thermodynamic critical conditions, at very low temperatures, under strong electric fields or in situations involving extreme gradients in the boundary conditions. The goal is to gain a profound physical understanding of the essential processes, which is the basis for new analytical and numerical descriptions and for improved predictive capabilities. This joint initiative involves scientists at the University of Stuttgart, the TU Darmstadt, the TU Berlin, and the German Aerospace Center (DLR) in Lampoldshausen within 18 projects. The present contribution provides a brief overview of the structure of this CRC, of projects being carried out at the SFB-TRR 75 and some scientific highlights of selected projects. The main purpose of this article is to familiarize colleagues with this extensive and dedicated research effort in this area of drop dynamics and to motivate further collaboration with others in this field.