New and more accurate techniques for satellite gravimetry will be available soon, with promising applications in Earth sciences. With this special issue the authors want to stimulate discussion among Earth scientists on objectives and preferences for future satellite gravimetry missions. This is an urgently needed discussion. Visions for follow-on missions have to be developed today, if they are to be realized within 10 years, given the required preparation time of such satellite missions.

The authors have played key roles in gravity field research, and in particular for the preparation of the current gravity field satellite missions CHAMP, GRACE and GOCE. They are members of several mission advisory boards. They presented their work with many contributions at international conferences such as EGU, AGU, IUGG.